Uber is very new in Belfast and I wouldn't be too sure about their drivers skills as a city guide.

A taxi from BFS to the city centre is about £25 depending on traffic. There is a taxi company operating out of the terminal building but they are more expensive.

Belfast has 2 major taxi companies (Fonacab and ValueCab). You would have to call to pre-book but they always have cars near BFS and you will be perfectly safe with either. They also do city tours which cost (I think) about £20 per hour.

There is a regular bus service to/from BFS which will drop you in the city centre (£10.50 for a return ticket).

There is also a bus tour of the city that you can use (just google belfast city sightseeing).

As for restaurants and bars.....the Cathedral Quarter has lots of both and you can easily walk around the area and see what takes your fancy. There are a few more upmarket restaurants around the City Hall area - Meat Locker, Love Fish, Coco, Bar + Grill at James Street South and Eipic (Michelin *). Ox is another Michelin * option.

Happy Travels.