Just returned from Panama City. Some notes about what we would recommend, and what we discovered:
(0) Four Days: Panama City is a "small" place, in that the many things you could do are really half-day deals, including the foremost attraction, the Miraflores. We felt we were there at least 2 days too long, for our week-long stay. Better to plan a 3-night stay on the Caribbean side, or on Las Perlas. Unless, of course, you want to go for the deep-sea experience on the Pacific side. Deep sea fishing is supposedly a big deal here. There are many such vessels at the Causeway marina.
(1) Taxis: Plentiful and cheap, especially if you hail from the road rather than relying on hotel staff or concierge-supplied lists. The drivers who serve the hotel/ condo set speak English and charge at least double. Hail a taxi and negotiate the rate by asking ahead how much they charge, and you usually get a much better price. Taxis charge by zone and by headcount. If you are near the edge of a zone, walk past it and get a better rate. If your party is more than 2 - 3, expect to pay extra per headcount. Taxi drivers sometimes change the rate mid-ride, but often for cause, like an unexpected road block (we encountered a protest one day.) Taxis can become scarce at commute hours so plan accordingly.
At the airport, go to the upper deck where the departures are and hail curbside. You can avoid the hustlers downstairs. Expect to pay $28 for 3 people from Tocumen to center of city. More if there are more in your party or if you are going farther.
You can also hire a driver by the hour. For this I suggest using an English-speaking guy (they are all guys,) since they can flex with you and tell you about history/ politics/ local conditions as you drive around. Top rate is $15/ hr. We paid this rate for a group fo 6, which is "reasonable". Any hotel concierge will have a roster of drivers.
(2) Construction: It is everywhere, except on the Causeway and at Cerro Ancon, as far as we can tell. The Bella Vista area is a hazard to walk through for the construction, and sidewalks are dangerous with the many uncovered, HUGE manholes or potholes. Casco Viejo is also covered with construction, as the country tries to pretty up an "exclusive", posh tourist area. They are going to move the poor people who surround Casco Viejo to a different location, and turn Casco Viejo into a pedestrian-only section. Expect construction noises as early as 6 am.
(3) Weather: Hot between 1 pm - 3 pm, but can extend to 12:30 pm - 4:30 pm. Plan to do little during the hottest period. Luckily most of the excursions are half day affairs. Breeze picks up at 5 pm and it is very pleasant in the evenings.
(4) Bugs, Sun & Drinking Water: Not much mosquito problems at all. Sun is hot midday. Wear sunscreen by all means, but I have been surprised by how little tan I got, and I tan easily. Water perfectly safe to drink. Buy the tropical fruit drinks by all means, They are a treat. The local rum is made from cane sugar so light in color and taste, and cheap at $6/ bottle. Buy fruit juices and mix for your cocktail hour.
(5) Birds & Wildlife: We saw a sloth, hawk, iguana and birds at the Metropolitan National Park, and monkeys and birds (including a family of toucans) at Cerro Ancon where we stayed. Bird watching is between 6:30 am (or earlier) and 8:30 am generally, but my husband saw the toucans at 9:15 am one morning.
(6) Cell Phone: You can get a pay-as-you-go phone for $25 - $30 and buy time as you go, in $5 increments. You can reload using your phone with a passcode, or at a store, or even online if your bank card works (ours didn't for that purpose.) Mas Movil is the most pervasive service. You get lots of promo offers by text, but in Spanish. Get a concierge to help you figure out what would serve your needs. Get the phone in town; the airport store is too expensive.
(1) Miraflores: A must-see. It is one of the 2 locks on the Canal open to the public, and the one that is actually in PC. The museum is fabulous (four floors and lots of interesting technical info and history about the Canal.) Plan to visit this in the afternoon, as the ships come through the lock beginning around 2 pm. Reserve a table on the deck outside for the best view of the lock in operation, without having to fight the upper deck crowd for a view. You pay $34 pp for a buffet, but can also order ala carte for under $20. Many taxis serve this area so you can hail one to and from; no need to contract an English speaking driver for this.
(2) Casco Viejo: A beautiful colonial area, which is perfectly easy to navigate without a guide if you went with a tour book in hand (Frommers and Lonely Planet both offer a walking tour guide for this area specifically.) Note this place is for the very rich, and for government offices. It is an area that has experimented with a "mixed neighborhood" concept during Noriega's reign, and thus still has pockets where derelicts and homeless people hang out. Just be a little vigilant if there are just the two of you, and you will be fine. Police presence is very widespread here because of the government presence. It is a beautiful colonial area that interested our architect friend a GREAT DEAL. He went back 3 times during our week's stay.
(2) Causeway. Walk the entire length of the Causeway, which cools down with strong breezes in the evening (~ 5 pm.) Shop at the craft stores on the second island, or have a drink and enjoy the ocean view. Mi Ranchito, almost the first restaurant you encounter on Naos Island, is a great seafood place that is very reasonably priced. Great ceviches and sea bass (we ate many courses of corvino while in Panama.)
(4) Metropolitan National Park is a rain forest inside PC. A very compact rain forest experience and, if you are lucky, you can see a sloth, many kinds of birds, all in less than 3 miles of walking. Go early in the morning if you are serious about birds. There are many here. Just make no noise and settle down every so often so they will come out. This place has the feel of the cloud forest of Parque de Amistad near the Costa Rica border, but is much more accessible.
(5) Sobrania National Park (Pipeline Road): If you are more ambitious, visit this park, which is 45 minutes away by car. You can contract a drive to pickup and drop off for $100 for 6 people. Less for fewer people. The Pipeline Road is internationally famous for birding. Go early for the birds. We also saw groups of monkeys high in the trees, and heard the howling monkeys (but didn't see them.) Many, many birds. This one deserves a guide for the flora and fauna. But we couldn't figure out how to hire one at a reasonable price, since they charge by headcount and we had a big group. So we went without one.
(6) Cerro Ancon: If you are a walker, this hill is a nice walk that affords a good view of the City at the top. Also a mother and baby nigh monkey in the bamboo grove near the guard house (ask them to show you the monos,) and a family of toucans at the very tips of the tallest trees 3/4 of the way up. You will need binoculars for those. Interesting tidbit: some 70% of the waterfront residential towers are vacant. The construction is funded by money seeking to be laundered!
(7) Fish Market: Boats come in at 5 am and 8 am, if you want to buy seafood. Amazing langostinos (large shrimp) and fish, as well as clams etc. Otherwise plan a morning visit to enjoy the ceviche from the sidewalk stalls. Good photo ops if the wholesale trade is still open when you go: they close before 9 am. Wear close-toed shoes.
(8) Crafts: The Kuna people sell their crafts at two concentrated locations: one in the Balboa area 3 blocks south of the YMCA, west of Cerro Ancon. The other on the second island on the Causeway. The same people operate both locations and move merchandise back and forth. The Causeway is a bit more expensive.
(9) Pedestrian Shopping/ People Watching: La Central is the place for CHEAP (read the merchandise is not of high quality either) shopping in Panama. It is near the waterfront in the San Miguel district of Panama City. Open 10 am - 10 pm – but this is a poor district and visiting after dark is not advised for gringos. I would suggest not to go with too much cash, and leave your passport at home. I had my hand firmly on my waist pouch the whole time we were here, but the street definitely looked colorful. More suitable for people watching.
(10) We considered visiting an island as we ran out of things to do. But the mid-day heat and the difficulty of transport stopped us.
(11) Monkey Island and Embera Village: We opted not to do these two. The former because this forum advised that the monkeys have run away, and the latter because we didn't think it would be an authentic experience. Indeed our driver told us the real Embera villages are farther up the mountain. The one for tourists are just that: operated for the tourists. For the real Indian experience, visit the northeaster Caribbean side.
(12) Las Perlas: Wish we had managed to make the right reservations and visited this pearl of a place.