I've always accessed the Maze by packrafting across the Colorado River at Spanish Bottom- You drive into the Needles, then it's only a 8 mile hike down down Red Lake Canyon, and quick paddle across the rio to The Maze. Beats the LONG abusive jeep drive in, and works in some of the Needles country, which is fantastic. I use a cheapo Sevylor Trail Boat ($100, 3lb) for the crossing and hide it by the river for the return.
There's a few good routes and trails in the Maze, but if you want to occupy a few days or do a longer hike, you'll likely end up doing a fair amount of jeep road walking and/or carrying a lot of water- A cursory look at the Trail Illustrated maps will yield many possible treks, just check with Hans Flat about water.
If you haven't been, I might check out the Needles District, which has the most trails, several of which make good loops or don't require a lot of water- Salt Creek is especially nice.
A couple seasons ago I did a 15 day circumnav on foot and packraft around the whole park including all three districts and it was great. I have some route info and link to pics here:
The Maze is amazing though- The Overlook Trail is one of the neatest trails I've ever seen, and the Harvest Scene panel is some of the finest rock art in the Southwest. PM if you want specific details.