I discovered recently as I was preparing for a tournament with many games I didn't know that there are not too many strategy articles on the geek for some games. My objective here is not to provide a detailed analysis of the game, only to give a newbie a very basic outlook of general strategy.
Balloon Cup is a fairly simple game that focuses mainly on tempo. You need to claim 3 of 5 colours to win. The big thing that you should focus on is ensuring that you never spend a turn putting a balloon down on a race that your opponent is going to win. Pick your battles, and whenever possible ensure that you have cards that guarantee a win in your hand before you start playing cards on a race. Lastly, remember the rule that the next turn goes to the loser of a race. That can be very useful if you need to cycle a card.
Interesting. I disagree with some of that, although it might depend on whether you are playing with the publisher's rules or the designer's rules. We always play with the designer's rules (or a variant of them), which disallow playing on the other side of a tile until your side is full. That forces more interesting decisions, and often puts you in a position where you have to play the least-bad card in your hand.
Perhaps because of that, I often toss middle-value cards on a losing race, just to get them out of my hand.