Disney

"Here are my 2 cents, based on probably 8 or 9 trips to Disney.

1. I have stayed both on and off site, and while some of the "Disney" hotels are amazing, I think the "value" Disney hotels would really disappoint you, especially for $155/night (I assume you are talking about Pop Century and the "All-Star" Resorts. If you aren't going to stay at least at their "moderate" level resort, its not worth it (and even then its debatable!).
Something you should know - unless you are staying at the Polynesian, Grand Floridian, or Contemporary Resorts ($$$$) you would have to drive to the parks anyway, or take a bus. I would recommend touring some of the nice hotels while you are there - its lots of fun, and you can dream, right?

Back to the real world, we've stayed several times in one of the Hampton Inns right outside the main gate, which is less than 10 minutes to any of the parks. Rates are usually great and include breakfast, which would really add up at any Disney hotel, even the "cheap" ones. Quality is above Disney's "value" hotels.

2. Parking, like I said, you would have to deal with this anway. Its inconvenient in the sense that you must park pretty far from the entrance to the park and take a "tram" to the entrance, but Disney has it down to an amazing science and once you get the hang of it you realize they do a fabulous time of moving all those people. As for price, I think it’s about $10/day, but you'll save way more than that by staying off site.

3. I've never driven south of the Kiawah/Charleston, SC. so I'm not much help here. South of the Border can be fun if you've never been there. Its right on i-95 between NC and SC.

4. Unfortunately there's really no way to avoid crowds - however, some strategies we've used that seem to help are when you enter the park go left instead of right (most people go right) or start at the back of the park and work your way to the front. By mid-day the crowds will be the same everywhere, but this should help you out for the morning. I doubt Christmas Day will be any different from the others - the whole week is very popular.

5. Park hoppers are a hard call. As an older child/adult, I've always gotten one but usually we stay 5+ days, so more days than parks and you want to go back and do all the "good stuff" again. With a small child, you may find that one park for all (or even only part) of the day is all you can handle. Think realistically about your child and the grandparents stamina. If you are going home mid-afternoon/early evening vs. switching parks its probably not worth it. Also keep in mind that switching parks probably takes at least an hour and a good deal of hassle, especially w/ a baby & stroller, whether you move the car and deal with the parking trams or take Disney bus/ Monorail. You may not want to deal with it.

6. Again, its hard to know your family. I've never been for less than 4 days and prefer 6-7, but we LOVE Disney. I would say to go for the 3 days, especially if you aren't going to do the park hopper. Plus you don't want to spend more time on the drive than in Disney!

7. Meal Plan is a TOTAL waste. Eat breakfast at your hotel (free), lunch at the park (but at "off" times, ie: not between 12-2) and then for dinner you can stay at the park or eat somewhere "off property" for a lot less."