Teen Attractions In Or Around The City Of Cleveland, Ohio For A Sweet 16 Party?!

I'm looking for a fun, reasonably cheap place to hold my sweet 16 party at. I'm turning 16 on January 17th, so I'm hoping to have my party the weekend of Friday, January14th-Sunday, January16th. Maybe even Monday the 17th because there's no school (Martin Luther King Day.) I'm thinking somewhere with entertainment (karaoke, dancing, games, etc...type of thing) and we would just bring our own food or eat at my place after if needed.
Are there any places in or close to Beachwood, Cleveland Heights/University Heights, Mayfield Heights, South Euclid/Lyndhurst that would be good for a sweet 16 party?
Also, money is VERY tight, so somewhere with decent pricing or negotiable pricing?
Keep in mind, it will be WINTER, so the roads will be a bit tricky, and I live in an apartment so I couldn't really do anything at my place.
All helpful information is appreciated :))