I have rested multiple times, both outside and inside the city, and I am unable to replenish my spell points, am I missing something?

Two probable causes... first, do your characters have enough food? If they don't have 1 unit of food each when they rest, resting will not recover health or magic points. Food can be purchased cheaply in the tavern in the first town, and found for free in certain other locations.

Second, are your characters diseased/sick? I'm pretty sure that that condition will prevent spell points from regenerating when you rest. You can cure it at a temple; the temple in the first town is cheapest.

I just wanted to thank you for your post! At first it was just one or two characters who wouldn't heal, and then their spell points wouldn't regenerate, and then no one's hp/sp would reset upon resting! I'd completely forgotten that these guys need food! Thanks very much! I was despairing that I'd have to quit, but now I'll be fine, as long as I remember to keep these guys in victuals.

Thanks very much!
Leandro

Some Roast Peasant is what your characters need.

Or you could Fly to the desert and pick up some food at the oasis. (The fact that the enemies are probably too tough for you is irrelevant, and there are two ways to cast Fly even if your level isn't high enough.)

Edit: One random thought: What if you have a character drink a Max HP potion, deprive that character of food by trading food, and then rest? Does the character's Max HP go back to normal, or does she keep the extra HP? (Maybe I need to start up this game to check. Fortunately, I know how to kill the Cuisinarts with a party that's just starting out, so it wouldn't take long.)