I would go with Florida, personally I would choose Orlando because you can get a house with a pool for relatively cheap. However Miami has kosher food and guaranteed minyanim.
Flights from Chicago to Orlando on SW would be about $250, on Jetblue it should be about $275 although you could probably get a better deal if you do some more research. Pool homes can be found for $750-$1,000 per week . Try Florida Gold Vacation Homes, Orlando Pool Homes, or homeaway.com vrbo.com etc.
According to your budget this would leave you some extra for activities
Have fun!