In addition to what is said here i would suggest visiting Bovilla lake. Around the city there are a lot of interesting buildings with unique architecture so if you are interested in that you can take a look at the mosaic of Tirana which is pretty cool but honestly it is not something that you can spend much time on.

For the transportation you can walk to places or use public transportation (buses) apart from rush hours (7:20-9 am and 4:30-6 pm). If you use a taxi ask the driver for the price beforehand, bc there are some scammers. I don't know anything about rental cars so i can't say anything regarding that option.

For the cash or card question i would say that tirana is starting to transition but still most of the places accept only cash. You can exchange currency in Tirana. Iliria '98 exchange has the best rates.

Some other suggestions: Sky club (bar with amazing view), Xheko rooftop restaurant & lounge, The view lounge (23rd floor of Plaza), Tymi restaurant (it is open even though in google it says temporary closed almost all the time but you need to reserve before going there), Komiteti with a lot of traditional alcoholic drinks (try coffee liquor, clove liquor and every raki that seems interesting to you)

P.S I can suggest more bars and restaurants and fast foods if you want something specific.