Find a flight. Think outside the box. If you know anyone in the airline business, you may be able to get a buddy pass, which will allow you to fly inexpensively. If you are 18 to 22 years old, call AirTran and ask about its student standby tickets. If you find a flight, proceed to Step 3.
Stock your car. If it will be a long trip, bring books on tape or CD for the driver and books, video games and DVD players for the passengers. Pack snacks and sandwiches to avoid expensive food stops.
Find a hotel. Although many websites will help you with this, Expedia.com generally has the cheapest deals. Enter your dates and location in the Expedia database, and it will find the cheapest hotel options.
Plan entertainment. There is plenty to do in Panama City. For your weekend trip, you may want to buy cheap snorkeling gear or an inflatable raft for hours of free beach fun. Check out St. Andrews State Park. It offers beaches, nature trails, fishing--plenty of entertainment without the tourist-trap price.
Avoid the glitz. You will blow the most money if you are charmed by the large mini-golf and arcade places, the huge souvenir shops and the airbrush T-shirt joints. Stick to the entertainment that nature provides, and your budget will thank you.