There're two premier inns in the city centre IIRC. One nice, one not. If you're looking the one on King Street is good. In the centre of town but a nice part, next to the river, good eateries around there.
Going out, depends what you like.
Clifton, whiteladies road are good (pick and choose on Whiteladies, personally I like Bar Humbug).
Avoid Beirut in the centre of town (floating harbour area, you can't miss it...well it's not "floating" as such) Corn Street is shite too, but it's all down to what you like.
Closest I ever got to that area is the Triangle/Park St where there's some OK places, Embargo?
Fair few bars open late, like til 4 maybe later IIRC.
Zero degrees I like a lot, has it's own microbrewery. Good food.
Three sugarloaves (?) is a good pub.
Thekla is a riot

...depends what you're into really