It could also be useful for you to know if you take the tram right till its last stop, Karatas, that it is also a stone's throw from the Dolmabahce Palace - the one the last sultans built to impress.
The stunning Imperial Hall there features a contribution from Queen Victoria - an amazing 4.5 ton Bohemian crystal chandelier (which is only switched on these days perhaps a couple of times a year when dignitaries of the highest caliber are entertained, with Sean O'Connery being the one granted that honor last year).
You can thus combine the trip to Taksim with a visit to Dolmabahce. Speaking of views from the tram, try also not to miss (on your right - as you near the embankment from Sultanahmet) the Sikerci railway station and the small steam engine outside it, which used to haul the original Orient Express.
Another way to reach Istiklal is to take the same tram - but alight immediately after crossing the Golden Horn by the Galata Bridge. The stop, I believe, is called Karakoy. The Tunel funicular subway (the world's second oldest operating underground after London's Tube) is a couple of minutes' walk from there and will take you to the other end of Istiklal from Taksim Square in an instant. The avenue is a pedestrian precinct, but you can still ride the whole length of it for fun aboard a "nostalgic" tram to Taksim (or the other way round).
When in Istanbul recently, we just bought one akbil pass for four of us for convenience's sake and initially charged it with 50 YTL (excluding the refundable deposit, which is 6 YTL, if I am not mistaken), but later added another 10 YTL.. So you can figure out for yourself how much money you will need on your akbil. These "buttons" are also good for ferries and buses. We had some money left on our akbil at the end of the stay, but we turned in that contraption and got all (well, almost all)) of our money left on it back.
PS. On another subject (which I recall as I think back about Istanbul) - I only have one serious complaint))) about the city and, being a Briton, you will perhaps sympathize with me. They have great street food out there (macherel sandwiches grilled right on a small boat moored at Eminonu are a must), but almost none of those eateries offers lager, let alone ale. Spent quite some time in some locations (for instance, on the Asian side) looking for outlets where they serve lager (as I do not drink milk and so would not have the milky drink ayran they offer everywhere, though my wife and daughter enjoyed it). On the other hand, freshly-pressed pomegranate juice (no problem with finding that) is a fine (and much healthier) alternative to Efes. )))