It's really not much of a walk at all up to the main centre, 5 minutes walk. The tram would cost you 90p (though sure you can use an over 60s bus pass on them if you have one) just for a short hop, not really worth it.
There are 3 free buses now, 2 of which go from Piccadilly Station (Number 1 which is orange and 3 which is purple):
http://www.gmpte.com/buses/metroshuttle.cfm
What kind of things do you like doing and what kind of budget are you on? I live here so can give you suggestions based on what you fancy doing from eating places, coffee shops to things to see.
They do quite a few walking tours you can book onto which cover all sorts of things.
For something special, there is afternoon tea (or a cocktail!) at Cloud 23, a bar on the 23rd floor of the Hilton with floor to ceiling views over the city.
http://www.cloud23bar.com/
There is a big wheel in Exchange Square (near where the bomb went off) and The Wellington pub is facinating as they picked it up and moved it bit by bit after the bomb - it does really nice food too.
http://www.beerinthee...ington_Inn/Manchester
The two Chop Houses (Sams and Toms) are also good for good more traditional food in a pub like setting. You may need to book at Sam's especially though. For more of a bargain, The Shakespeare does lovely homecooked pies with chips/potatoes and veg for a bargain £4.95ish! It's down a side street next to Primark.
Even though the