Provence & Riviera OR Burgundy & Alsace?

Very different areas so depends on your interests. If you're into vinyards and pretty countryside, then Burgundy and Alsace are a good choice. Beaune and Colmar are good towns to stay in and 5 days are enough to see the highlights. Provence and the Riviera cover a wider area so you'd need more time there. Lots of Roman history along the Rhone; Avignon, Ax-en-Provence, Nimes, and Arles are all worth a visit.
Being from Surf City you'll be disappointed with the beaches on the Med.... lots of pebbles, not much surf and very salty water. The hill towns overlooking the Med are interesting to visit. The beachside cities are too touristy for me but you may like them. Antibes would be my choice for a place to stay.

You need to decide what you're looking for. If you're into wine, then, hands down, Burgundy and Alsace are the way to go. Both have excellent Routes du Vin, and the wine is consistantly better, IMO, in either of these places vs. down south. Biking in Burgundy through the vineyards was a highlight of our trip (gentle rolling hills, no traffic, great wine. What's not to like?). Alsace will also give you a taste of the Franco-German culture, which is really cool. Great beer, too. If you want scenery (i.e. A Good Year style cinematography), then Provence or the northern region will offer that, but Provence is a bit more rugged. The wine's not bad there, either. If you're there during the Lavendar bloom, it will be absolutely stunning. I'm not much of a beach guy, so the Riviera doesn't appeal to me, so Provence is the real reason to visit the South.
If I had to pick one, I'd head north. But, I'm a wine guy, so this is one of the reasons pulling me there. You're also near bigger cities, and Cathedrals. I also head for Cathedrals...

A choice like this, between two pairs of two great regions, is ultimately personal, and you give us nothing to go on. On the other hand, you can't go wrong! Five days is enough to have a nice introduction to either pair of adjacent regions, and I think the pace (two destinations in five days) is brisk but hardly killing. You won't see everything of course. Logistical note: You will benefit from a car (or bicycle) in every region except, possibly, the Cote d'Azure, but especially in rural Burgundy. If you are truly indifferent between these choices, ask yourself which fits in best with the rest of your itinerary and go with that.

I've spent a fair amount of time in all these areas, and if forced to choose, would take Alsace and Burgundy. Beautiful scenery and villages, great wine.