Here are some advantages to staying offsite and onsite:
ADVANTAGES
Offsite:
+ Generally cheaper (the lowest Disney hotel has a rack rate of around $99/night)
+ Lots of hotels to choose from in the Orlando area
+ Some hotels have free continental breakfasts or free breakfast for kids
+ Some hotels have a free shuttle to get to the parks
+ You have the freedom to explore non-WDW things
+ Food is generally cheaper
Onsite:
+ You can get around WDW without a car (you can use WDW transportation)
+ Many people feel "Disney magic" when they are onsite
+ "Disney quality" rooms
+ You can charge purchases to your room key, so you don't have to carry around cash
DISADVANTAGES
Offsite:
- Hard to get around if you don't have a car and the hotel doesn't offer a shuttle
- Quality of offsite hotels can vary
- No "Disney magic"
- The tourist areas (I-192, International Drive, etc.) can have bad traffic during peak times (rush hour, park closing, etc.)
Onsite:
- WDW transportation system can be slow
- WDW transportation gets crowded and packed during the parks' opening and closing.
- More expensive than offsite options
- Food is more expensive at onsite hotels