If by cross trainer you mean between road and mountain bike, there's a bunch of choices out there; they're also called hybrids, but in any event $350 is going to make it tough. I don't have any brand recommendations, but I suggest shopping for a bike without a suspension fork--suspension forks on bikes this cheap rarely work very well and weigh a ton. You'd be better off with bigger, more plush tires and a suspension seat post (which such a bike might actually have).

Oddly, mountain bikes in this price range are pretty amazing. I recently bought a $360 Specialized HardRock for my 11-yr-old daughter (her first full-sized-wheel bike), and I can't believe how good it is; I'm actually going to buy one for myself and leave it at my inlaw's house in Maine. This bike has huge, heavy tires, so I swapped them for some dirt-only IRC folding tires I got on sale at Performance for $25 for a pair, and the bike lost well over a pound. You could put smooth hybrid tires on it for even greater weight savings, and it would handle pretty well on pavement.

-d

Get a Trek 7200FX. It seems to be a nice bike.

Paul