I can personally recommend two printers that handle short-run printing who I've used in the last few months: Thomson-Shore and Transcontinental Printing. Both have websites; both do quotes for free. T-Shore is in Michigan, while Transcontinental's short-run plants are in Quebec, Canada (good rate exchange right now means I get better prices from Transcon. at the moment).
I've done hardcover and trade with Transcon. and trade only with T-Shore -- both do quality work.
Check out your local printers and get quotes, too. Get at least three quotes for comparison. Be sure to give them all the pertinent info:
<dl>
<li>trim size
<li>page count (multiples of 16 or 32: each printer is different for signature counts, so check with them before you design & lay out your book!)
<li>paper choice for interior paper
<li>paper choice for cover (if trade]
<li>binding type (smyth, perfect, etc.)
<li>colors (interior and cover -- 1-color, spot, 4-color)
<li>print run (how many copies)
<li>shipping (more than one place?)
</dl>
You will need to get all sorts of info from your printer of choice before you design and lay out your book, as well as before you do your cover work.
You may want to consider hiring a production company to handle all of the above as well as deal with the printer. They will design and typeset your book, handle proofs, and neep printer neepery at your printer. It's the way a lot of self-publishing authors go, since writing is not the same skill sets as book production.
Write to me if you have further questions; this is what I've done for a living for 20 years (I produce books for the big publishers, such as Simon & Schuster).