The taxi ride from the airport to The Reefs Horel should take a very pleasant 35-40 minutes...around Harrington Sound, through the Tucker's Point golf course and along South Road, along Bermuda's magnificent south shore...with a few genuine '..take-your-breath-away..' vistas along the way.
One of the best '..excursions..' you can do is to arange for a private taxi-tour of Bermuda by one of its Blue Flag Tour Guides These tours usually run $50-60 per hour, with a three hour minimum (on average most tours will last 4 hours)...but they may be one of the '..best buys..' on Bermuda. If you were to find another couple at the hotel to share the tpur with you, they become a relative 'bargain'. Blue Flag guides (not every taxi driver is Blue Flag certified) are all VERY knowledgeable about all things Bermuda...and if you give them some idea of any particular interests you may have--flora & fauna, architecture, history, etc--they can usually customize the tour to suit. There is no central listing of these guide, but the front desk at The Reefs will probably have a list of several that previous guests have used and been satisfied with.
There really are no absolute '..Must Do..' excursions on Bermuda. Perhaps the best '..excursion..' will be to get out and about and explore the islands on your own. The place is only 21 miles long and 4 miles wide...so it's not as if you can be lost for very long...and often times being lost on Bermuda is half the fun. If you're so inclined, you can rent motorscooters and tour Bermuda on your own, along your own route, on your own schedule, stopping wherever and whenever as you go. The ubiquitous BERMUDA HANDY REFERENCE MAP is pretty much all you need.
As an alternative to motorscooters, the public transportation system is excellent, relatively inexpensive and take you to or near just about everywhere on Bermuda. If you purchase a multi-day TRANSPORTATION PASS, you will have '..hop-on / hop-off..' convenience..' for all public buses and ferries. You can make your own '..circumnavigation..' of Bermuda, by land & sea using the system...'hopping off' at likely spots along the way. It's worth noting that although The Reefs has one of the best private/hotel beaches on Bermuda...as good as it is, it doesn't hold a candle to many of Bermuda's public beaches. Take/make the time to visit these. There's good snorkeling among the rocks and broken reef just off of the beach at The Reefs...but perhaps the best snorkeling from the beach on Bermuda will be at the public CHURCH BAY, just down the road.
As for other excursions, there are several glass bottom tour boats that go out to the reefs; several snorkeling excursion operators; a couple of '..helmet dive..' operators; a couple of scuba dive operators; a 'day-boat' fishing operator; evening cruise operators;...etc. Which of the excursions and activities available to you will depend largely on your own personal interests and preferences. As an example, if you're interested in an entry level snorkeling tour, those offered by JESSE JAMES CRUISES are good...but not be so for more experienced snorkelers and divers.
Pick up a good guide book on Bermuda...or scan the internet for general Bermuda tourism web site to get some idea of what's available. Do some research, with your own personal interests and preferences in mind. You can start with the BDA Dept. of Tourism web site, which is fairly comprehensive.
As for '..romance..'....well that's something that you tend to bring along with you...or not. For some, '..romance..' is a dinner served at a torch-lit table down on the beach at The Reefs...or...a simple picnic on one of the little, semi-secluded public beaches just down the road. Both offer surf, sand, starlight....and the potential for '..romance..' Which you choose and what you do with it is pretty much up to you. For some, room service for two by candlelight (a short candle in a tall glass keeps it lit in a breeze) and a late wake-up call, followed by a room service breakfast does the trick quite nicely.