A flying visit to Manchester

OK, Mancunian UKY-ers.  I will be in Manchester next Tuesday-Wednesday (26/27) but I will only have a few hours there.  Barring train delays (which you can never really bar) I will arrive about 2pm and I leave at 1pm on Wednesday.  Tuesday evening I have a professional thing from 6-8.30-ish.  With this timeframe in mind, what would you recommend to see?  I will be staying near the train station (Piccadilly) and I don't know Manchester at all, so I'd rather not go anyplace too far away.  I like art and history, local products, and independent coffee shops.  Also, I need a place to eat that's not hugely expensive. 

Any recommendations gratefully received!

Not a local, but I would recommend the Whitworth Art Gallery (Univ. of Manchester)

Too bad you don't have more time.
I'd recommend local beer at the Marble Arch in the Rochdale Road.
The tile-work on the walls is beautiful... just watch that sloping floor!
http://www.marblebeers.com/

Do you like art? The Manchester Art Gallery has some gorgeous paintings (and is in the city centre), and I would second the Whitworth, which has more of a textile/installation focus.
The Manchester Museum (Natural History/attached to the University) is also good fun if you like to wander round.  I love Albert Square (in front of the Town Hall) as a place to sit and people watch, and if it's nice outside, the Oyster Bar (near the Arndale) is a cheap place to get a nice pint in the city centre.

There are loads of excellent restaurants.  There's an Armenian restaurant just of Albert Square (down some stairs) that is pretty good and reasonably priced. There is loads to eat in Chinatown (and, actually, a Korean place right near Town Hall (same side of the road as the Armenian one, I think) that is pretty tasty as well.)

The John Rylands Library (Deansgate) is stunning, and they often have cool exhibits on. They also have a nice little cafe attached that is fun to people watch from as it backs on the entrance to the crown courts and, well, sometimes it can get a bit...interesting? when people continue their arguments outside.

Hmmm.  I can keep going, if you like, is there any particular food you were interested in?

This just appeared on my Facebook feed (courtesy of a friend at the John Rylands)
http://www.guardian.co.uk/travel/2013/feb/15/quick-travel-guide-manchester

I only know Manchester as a tourist & for passing through on the way to the airport. But Jennie's suggestions are sound in my opinion!

The Manchester Art Gallery has a great collection of Pre-Raphaelite paintings, and just a smidgen of Lowry - free admittance too! Albert Square is nice - I've eaten at the Armenian restaurant and in Chinatown, both yum & well priced.

I've had breakfast/coffee at Trof - in the hipster Northern Quarter, an area with lots of other inviting/interesting places here & there. Also did breakfast/coffee at Cornerhouse.

We are going back to Manchester for a weekend in April.  Here is a recent Guardian article - Local's Guide to Manchester. We are keen to try some of the places mentioned there!

ETA - When we recently went to the Harrogate spa here, we ended up in a jacuzzi with a couple from Manchester who were visiting/touring here in Yorkshire. The husband said we must go & eat at Cicchetti when we are on our Manchester weekend, so that is another one we might try - looks like they do breakfast & afternoon tea as well as regular meals.

Thanks so much for the suggestions, everyone!  I think I will definitely go to the art gallery, and will investigate the other suggestions for coffee/meals.  You guys are the best!