Obviously will depend on what they like to do, but......
You can spend quite bit of time wondering round on foot (free).
If they are shoppers then within spitting distance you've got Selfridges and the big shopping centre there, then the markets (indoor and out).
St Martins Church is historic and remains in the heart of all the new build.
Wander through 'Grand Central' (above New Street Station) - recently opened and very nice.
Then go up along New Street and you'll come to Victoria Square, and be able to see the Town Hall (a concert hall) and the Council House (er... where the Council meet) and some statues and just quite a nice bit to wander through.
On what appears to be the side of the Council House, is Bham Museum and Art Gallery which is free and worth going in to - they usually have some child friendly galleries in the school holidays, and have stuff like the Egyptian Gallery, and it's just nice to see the massive paintings even if you aren't really in to art. They have an 'Edwardian Tea room' in there which is nice for lunch.
Then on from there (lot of building work going on at Paradise Circus so not sure of the exact route but it will be signpost) go on to the new Library. Really nice building. Go up to the higher floors and see the Shakespearian Library and there are two (I think) outdoor rooftop terraces you can go and view from.
That is Centenary Square - the Library joins up with the Rep (thatre) then you get to the Symphony Hall. Go through there and you come out by the canals.
You could do a barge trip, or just wander along the towpath for a bit.
There are LOADS of places to eat by the canals / going into Brindley Place.
Sea Life Centre is in Brindley Place but I reckon it is a bit of a waste to go to sea life centre, etc in a new city as they are the same all over.
If you turn right, rather than left in front of the Council House you can wander back to the Cathdral if that is your sort of thing.
If you make your way across to the Mailbox, it's quite an odd place. Some 'exclusive' shops and loads more places to eat.
The BBC have a place in there and you can do tours - I think you have to book, but worth a google.
Think Tank is worth a full day - not cheap, but loads to do there.
Woth looking what is on at the theatres - we have The Rep, The Hippodrome, The Alex, and The Old Rep all in the City Centre.
A lot of people like to go to Cadbury World, but that isn't in the City Centre (although an easy train ride from it). You'd need to book a slot in the school holidays though.