I disagree with staying off property, only because there is a price to convenience, too. Look at staying in a value resort and go the very end of April, early May (we'll be there the first week of May!). That is "regular" season so prices are lower than in early April during Spring Breaks.
I do agree with driving though. Leave the day before you want to arrive and stay somewhere outside Orlando (we stayed in Kissimmee the first time we did this for around $50/night) then check in to your resort first thing the next morning. Your room probably won't be ready but you will get your park passes and you can enjoy a full day at the parks! Then kind of do the reverse when you leave. Hang out at the parks until around 3 or so, then get on the road and find a hotel somewhere on I-95 on the way home - Savannah, GA is only about 4-5 hours from Orlando.
Plus, if you drive, bring a cooler and keep in the room with bottled water, drinks, etc. Plus, while you're on the road, you can keep sandwiches, drinks, etc, in there to cut down on the cost of stopping to eat on the way. We just refill our cooler with ice each morning/evening at the resort and keep it stocked. You can also pack pop-tarts and breakfast foods, snacks to take to the parks, if you drive.