As others have said, Ancoats or the Northern Quarter are probably the best options. There's loads of bars and some decent pubs. You will pretty much find all types of places around here and everything is very close by too. You won't really need to get taxis I wouldn't think as Ancoats and the NQ are next to each other. You could walk from one end to the other in about 20 mins. There is the Metrolink which will take you around the centre and over to Castlefield and Salford Quays and runs till late-ish but I'm not sure on the exact times. Uber is great for getting around, but be wary of the surge prices.
Personally, I'd avoid Deansgate. It's not a bad area, but pretty much everywhere else is much better!
Ancoats has Cutting Room Square with plenty of bars and is worth a visit.
If you're here for the weekend and fancy a gig on Saturday, it might be worth having a look at The Castle on Oldham Street as they have bands on in a very small room. It's normally a decent night in there and the drinks are really good and you get a good crowd in there.
Mackie Mayor is a great place as well - it's basically an old market converted to a food/drinks place. Plenty of options on beers, drinks and food and it's very nice on the inside.
If you're looking for an old-fashioned pub try The Peveril of the Peak, Britons Protection (great if you like whisky) and The Marble Arch (has a microbrewery) too. They are all a small walk from the Northern Quarter but worth a trip if you're into older places and ales/whisky. They can get quite busy mind.
Castlefield at the end of Deansgate is nice for a walk around as well if you need a bit of air to clear the head the day after :)
To be honest, you can't go wrong it's a great City! :)
