Taiwan in October and November is perfect. You miss the heavy summer heat and the monsoon rains, leaving you with clear skies for hiking mountain trails or hitting the night markets in Taipei. It is the best window to see the island while the weather stays comfortable.
For a trip costing around $2600, you might want to spread the payments out rather than hitting your bank account all at once. Using the Citi Simplicity® Credit Card, you get 0% for 18 months on purchases and balance transfers from date of account opening. This lets you pay off the trip in manageable chunks over the intro window on purchases.
Remember that the 0% intro window is a deadline, not a gift. If you have any balance left after the 18 months are up, the standard interest rate will kick in and start adding costs to your total.