Prague in May is perfect. The mornings are crisp enough for a light jacket, and the crowds haven't peaked yet, making it the best time to wander the Old Town without feeling rushed. You will want to spend your days walking across the Charles Bridge and exploring the hilltop castle grounds while the city is in full bloom.
To manage the $3000 cost, we can look at the Citi Simplicity® Credit Card. It offers 0% for 18 months on purchases and balance transfers from date of account opening. This lets you spread the cost of your flights and hotels over that 18-month window instead of paying it all at once.
Remember that this 18-month window is a deadline, not a gift. If you still have a balance after the time is up, the card will start charging interest on what remains.