I'm 27, lived in KC since I was 22; here's my two cents:

First off, I would recommend grabbing trolley tickets for $10 each on Saturday night. You can ride it all night and it will take you to various bar districts to see more of the City and visit more areas of the city. Plus you can take booze on them. Anyway...

Bar districts:

Power and Light: fun in the summer, it's not really a spot where locals spend much time. Like mizslu said, it's pretty touristy/flashy, but it will be fun for a night for a group of visiting guys. PBR Bar usually has some decent ladies. I don't know what it's like on Thursday night; but there will probably be some free show going on there tomorrow night (usually are on Fridays in the summer and they can be pretty fun). But just FYI, these bars are overpriced, loud, and usually packed on weekends.

Crossroads: Not so much a bar district, but it's just south of downtown and there are some decent restaurants and bars. The Cashew is kind of a cool bar, but it's pretty low key and isolated from other spots.

Westport: Few miles south of downtown; popular spot for fresh out college/younger people. Lots of bros, mix of laid back sports bars and hipster spots. Usually some live music at various spots on the weekend. Harpos and Kellys are probably my favorite bars out there. I'm pretty sure Harpos has a good drink special on Thursdays and it usually gets pretty rowdy in the summer. You guys could have a good time out here, though no guarantees if you are looking for ladies.

Plaza: Just south of Westport. There are a few bars down here, but it tends to be an older/wealthier crowd. Probably not where 9 guys want to spend the night on a weekend trip, but there are some decent spots to eat. Gran Falloon is solid spot to start your drinking and get some decent bar food, I just don't recommend staying out here for an entire night.

There are some other bar districts further out south such as Brookside and Waldo, but I'd probably skip those as they are more 'neighborhood' bar districts and can be pretty uninteresting. There is some stuff north of downtown as well, such as River Market, but I rarely venture down that way.

Restaurants:

Joe's Kansas City BBQ (formerly Oklahoma Joe's) - Kansas City, KS. Best bbq in town, call ahead or you'll wait in line for hours.

Q39 BBQ - Westport, Kansas City, MO. Best ribs in town, will probably be slammed all weekend but it's delicious.

Beer Kitchen - Westport, Kansas City, MO. American pub food; lots of beer. Small place, might be tricky to get 9 of you seated.

Minsky's Pizza - Locations all around KC. It's pizza. And beer. Best of the local variety.

Stroud's - Several locations. Pan fried chicken, delicious but you'll feel awful after eating all that grease.

Pierpont's - Union Station, KC, MO. Classier establishment, cool bar and location.

Grunauer - Crossroad, KC, MO. Austrian/German food. Classier establishment, my favorite restaurant in KC.

One additional note: Kauffman Stadium (Royals stadium) is way the hell out east so be prepared for that. Tailgating before the game is a thing, and pretty fun, but you'll want to get out of that area after the game as there is literally nothing to do around the stadium.

Have fun in KC!