I have run a couple of 5K's around Tempe Town Lake. You may have to do several laps but it is right next to ASU. It's nice a level and always lot of activity going there.

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Papago Park!

Tempe Town Lake has the paved running trail only along its south (downtown side) and north (Papago Park) side. And half of the north side is closed right now due to construction. So for the rest of the summer there is no way to "loop" the lake trail.

But never fear! just run 1 block further north and you'll discover a great little place that very few people take advantage of.

Just "across the river/lake/whatever" from ASU and Downtown Tempe. Run 1/4 mile across the Mill Street bridge and just head east and down into the LoPiano Bosque habitat.
http://www.tempe.gov/lake/Habitats/Habitats.htm[/URL" target="_blank">

(The Ironman Arizona actually just used this as part of their marathon course a couple of weeks ago).

It's a 2/3 mile long flat dirt road that parallels a nice little canal with lots of trees around it. The 202 Freeway parallels you about 100 feet to the south (and 50 feet up a steep bank). Find one of the bridges that heads north over the canal and you'll be in Papago Park.
http://www.tempe.gov/lake/images/Maps/PapagoTrailsMap.jpg[/URL" target="_blank">

You can run around the little buttes and in and out of the arroyos (dry stream beds). Some of the trails are really wide, mostly the ones on the ridgelines. But there are plenty of exciting singletrack trails too.

There's no way you can get lost. The 202 Freeway will always be to the south which you can still hear day and night. And if you cross any streets you'll have a high enough perspective to figure out where you are.

There is a drinking fountain in the little green park just to the east of Papago's desert terrain just below the tallest butte. Running on the Tempe side you'd never be more than a five minute run away from the drinking fountain. Look for the playground that looks like this:
http://www.tempe.gov/pkrec/parkfacil/images/PAPAGO%20PLAYGROUND1.jpg[/URL" target="_blank">

There are also public park restrooms at the northeast corner of that little park across the little pond.

There are enough little loops in the Tempe section to put in up to four miles without retracing your steps. But you can also head north across the street into the Phoenix section of the park that has similar trails but has more hills.
http://phoenix.gov/PARKS/hikpagud.html[/URL" target="_blank">

Weather in May should be highs in the upper 90's but with very low humidity. 100% sunshine. So even midday runs are beautiful as long as you stay hydrated. But don't underestimate that Arizona sun. You'll burn fast if you're not careful about protecting your skin.

Oh, yes. Understand that these are desert non-paved trails but very runnable. And you'll probably only have to share the entire park with some quail, some funny running birds, and a horse (and rider) or two.