Actually, you should have thought of these things even before you started coding.
Anyway, I don't think playing "mini games on a psp" is that good of a concept. If driving around is so boring, then why should I do that in the first place? I'm playing a game after all, I want to have fun. Why do I have to sit around and wait or play unrelated minigames? That doesn't seem so elegant to me. Either allow me to skip the drivingpart, or try to add something that makes sense (in a loose sense of the word) as far as driving is concerned. Car chases is a good idea. Races would be possible. In GTA, you get points for nice stunts. Why don't you add something like that?
Generally, if you ask yourself "What do I have to add to make Part X fun", then think if you really need the player to go through Part X at all. It might be enough for him to see a panel or a textmessage "After driving five hours through the desert, you're there". Of course, not all games are made to be "just fun", so maybe you're after that (in the sense of a realistic experience). If so, ignore what I've said.
(For some reason I keep thinking of that one game that had you driving a bus through the desert for hours without anything happening inbetween. I tried to find an article about it, but without remembering the name of it, thats hard

EDIT: Found something about it:
Link )