Deem Hills is one of the newer parks in Phoenix to open (2010) and as such a lot of people still don't know it's there. This means that it has much more of a secluded feel then some of the more well established trails around. It IS popular with mountain bikers though so be on the lookout for them as they like the more sparse feel as well.
Deem Hills is really 2 hills in one with a just under 6 mile circumference trail around both.
The parking lot for this side is on 39th Ave and Pinnacle Peak Rd. It's MUCH smaller than the main entrance for West side but, since it's lightly used, I've not seen it full. There is 1 ramada here and it has a water fountain if you need it.
This side of Deem Hills feels a bit different from the West side. Where the West side has a nice steady climb up and decent down, the East side goes up and down twice and and they both feel a little steeper than the West side. Like the West side though, the trail is nice and well cut through the desert. Be aware that it can still be pretty loose in places, probably because it is so new. This side is definitely for the average or above hiker, I think beginners would be cursing you if you took them here.
For a slightly shorter (and easier) hike you can take the Basalt trail for a shortcut that takes about 1.4 miles off.