Jack's (Front Street) and Financier (Stone Street or William near Federal Reserve) are my favorite coffee shops. There is Bin 220 on Front rated best wine bar downtown (because it's one of the only wine bars downtown!), it's not my kind of scene (overpriced, upscale, nothing special on the limited food front). Nelson Blue (Front and Peck Slip) is really popular because it's new, if you like a scene it's a good place to go. I like Meade's (Peck Slip and Water) it's usually more mellow, food is okay (not great) and you can sit outdoors. Meade's has the same owners as Jeremy's (ambience is frat house-ish, bras hanging from bar). Fresh Salt (Beekman) is nice, a lot of locals like it and reasonably priced if that is a concern (not a food place except for sandwiches). Head to TriBeCa or EV or LES for food. The Harrison (TriBeCa) is really good (not sure what your price range is). If you want to eat near the Seaport there aren't very many good places (you might want to do a search of this site for topic discussions). I usually eat at Acqua (outdoor cafe, fresh simple Italian fare) or Buon 'Amici (both on Peck Slip) or leave the neighborhood. Barbarini is good (more takeout kind of place). Il Brigante, read the posts I'm neutral on it. Tables Tales on water is one of the best lunch places (no liquor/wine). egit mentions Seaport North, most of the places I mention are in Seaport North neighborhood. I almost forgot, Spiegeltent is here! (NOT free like River to River). Lots of live shows and music, bar outdoors on East River with views of B. Bridge, restaurant (I'm not brave enough to try it, probably iffy, no responses to my related post on chowhound). Have fun and enjoy your visit!
I can't think of much in the way of live music in the Wall St. area, unless you've checked out the website for the River to River festival. There used to occasionally be live music at Jeremy's Ale House near the Seaport.
Wine bars -- there is a Divine Bar in the downtown area.
Not much in the way of coffee shops (other than the ubiquitous) Starbuck's. I like the Mud truck on Wall St. (near Water) or a cappuccino at the Leonidas chocolate store on Hanover Square (they give you a free piece of chocolate!).
You might check out the restaurants/happy hour scene on Stone Street. Other good meals include Harry's or the steakplace on Exchange and Broad (whose name is escaping me).
Keep in mind that much of the Wall St. area closes down after business hours. You are walking distance from many great restaurants in the Tribeca area, though.