I'll agree with what everyone else has said, and I'll add this:
On a tight budget, counter-service meals are the way to go. But I try to schedule at least one expensive, sit-down meal per trip, preferably two. My favorite is 'Ohana, in teh Polynesian (very expensive at $25.99 but well worth it to me), and I have also enjoyed Boma, in AKL, Liberty Tree Tavern, in MK, and Chef Mickey's, in teh Contemporary. LTT and Chef Mickey's are charachter meals; if you can swing a second sit-down, I highly recommend Chef Mickey's (it's also a buffet).
I also enjoy resort-hopping, or visiting the various resorts, as Stacey described. If you plan it right, you can see a lot in a short time without feeling rushed or hurried.
The easiest 3 resorts to see are the monorail resorts. Instead of taking the express monorail from the MK parking lot to the park gates, take the resorts monorail. It stops at each resort in turn, allowing you to get off and explore lobbies, gift shops, and grounds of the Polynesian, Contemporary, and Grand Floridian. Take some time to explore the Poly grounds; they are beautiful.
You can also catch a boat to the Wilderness Lodge from either the MK Resort Launch piers or from the Contemporary marina. WL is another fantastic place to visit and explore.
In the Epcot area, you can leave the park from International Gateway in the World Showcase and either walk or take a Friendship Launch around Crescent Lake to the various Epcot resorts - Yacht & Beach Clubs, Boardwalk, and Swan & Dolphin. The boat ride alone is worth the time, but each of the resorts is also within walking distance of each other and has a beautiful lobby and grounds to explore.
Animal Kingdom Lodge is the most remote WDW resort, located in the far southwest corner of the property and accessible only by bus or car. However, it is more than worth the trip! AKL has the most awe-inspiring, fantastically beautiful lobby of any hotel I've ever seen, and the savanah behind it is a place where various animals roam free for your viewing pleasure. Also located here is Boma, a wonderful buffet restaurant with African-inspired dishes (and the best prime rib anywhere at WDW!)
Even if you don't plan on spending much money, be sure to visit Downtown Disney for another pleasant walkaround. DD is a nice place with great sights and several great eateries and restaurants (hint: DO NOT eat at the DD Rainforest Cafe! If you'd like to try Rainforest, go to the one at the Animal Kingdom park, which is much better on both quality and service!)
If your trip is at the end of May, you might catch the first of Star Wars Weekends at MGM. If you're a Star Wars fan, these are lots fo fun. But if you're not, then avoid MGM while they're happening, because the park get pretty crowded.
Also in May you will catch the beginning of the summer heat. I highly recommend taking your own water bottle and carrier with you, because buying bottled drinks all day at $2 or $2.50 each will burn your budget pretty quick. Keep in mind that you can get a free cup of ice water at any restaurant or food service location to refill your bottle throughout the day; some of the counter-service folks will just fill your bottle up with ice and water for you if you ask. Keep hydrated! Dehydration will caus you to feel fatigued early in the day and you may wind up leaving early because you feel so tired and listless.
And above all, relax! It's our vacation, so you can proceed on your own pace and see, doo, and eat whatever, whenever, wherever you want, without any worries about others' schedules. Going solo is the best!
Also listen out when you get near the front of rides queues-the CMs will often shout out for single riders to fill carriages and you can often jump up the line quite nicely 
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