They want to sell their venue just as much as you want to rent it. I've had MORE success letting them know it's a videogame tournament up-front because then you can talk logistics. How many outlets? Where are they located? Does the venue have good internet for streaming? What's the policy like on outside food and drink? Do they allow photos/videos to be taken? (Most do, there are a couple that don't.) There are some venues that won't charge you anything (they'll charge you a deposit) but will take a cut from everyone coming in at the door. If they are doing that, find out their price -- a $20 cover is pretty prohibitive, but $5 isn't bad. Find out how late they can stay open -- I've been to tourneys where we've been kicked out at 11 and the bracket hasn't finished yet.
Be up front with what you are hosting. There is no shame in hosting a videogame tournament. And if the venue isn't comfortable with it, or perhaps they're out of your price range, ask them if they know any other suitable venues. They have more contacts than you do, let them help. If they are too expensive, but the hall would be perfect for a major or something of the sort, let them know. Tell them they might be a bit out of your range at the moment, but you'd like to hold events there once you've built up attendance.
The biggest thing: be completely honest, be completely up-front about everything.
