I see Papago as a starter location for trail runners and bikers alike. There's no hard hillclimbs/grades that will challenge a seasoned mtn biker or trail runner but there's plenty of good speed trails to hit cardio and do a nice tour of the park.
There's a tunnel under the road so you can go from north to south side of curry I think it is... I've yet to be over to the zoo but I know that's over there and as far as I know you can get a fairly good (free) shot of the zoo from there.
There's some good hiking stuff you can do and climb up into some cool caves/holes in the rocks.
I've been to an enduro mtn bike ride there on the east side and that's a good track for that, short but make lots of laps and you'll be tired after 4 or 5 of those fo sho.
Good park, clean, trails are nice - look out for bees tho sometimes! They've marked off some trails for that before but nothing new - you are in arizona.