I hate to be the bearer of bad news but here goes. If the only food service experience you have is doing a handful of dinner parties save yourself $13,000 and a lot of grief by not opening your own restaurant.
As others have said it is highly unlikely that you would get financing as restaurants are very high risk and without sufficient collateral it's almost impossible to get a loan.
Before venturing out on your own get real food service experience. Start at the bottom and learn every aspect of running the business from cleaning the toilets, cooking, purchasing, accounting, marketing, serving and inventory management to name a few.
While you are in the learning curve save every penny you can and add that to your $13,000 so have some capital to work with.
After you have this type of of experience and fully understand what it takes to run a successful restaurant look for restaurants for sale in your area, there will be quite a few. A lot business owners will finance the purchase for you, this is very common in the restaurant business, and a lot easier than trying to get bank financing.
I've been in the restaurant / bar business for more years than I like to admit and the biggest reason I have seen for failure is inexperienced operators. Get the experience, gain the respect of restaurant owners in your area, build your clientele while working for others and you should be on your way to success.