The other anon covered it pretty well. Right now is a good time for kayaking. Most of the creeks, rivers and lakes are full with snow melt right now so the water levels are high but the water temps will be cold at high elevations. Water levels begin to drop after the snow is all melted around May, from May to monsoons in July/Aug water levels are usually low across the state. Beware of flash flood during monsoon season and heavy rains though, 4 people have already drowned this winter in the Tonto. Some decent rivers and creeks I know are the Verde/East Verde, Upper Salt, parts of the Black during spring only, parts of the upper Little Colorado and several of its tributaries.The Rim and White mountains lakes are also great in summer if you stay away from the most popular ones. Do some research and you can find a lot more.
USGS, you can set it to show watershed boundaries and USGS stream gauges and lookup current/historical levels.https://maps.waterdata.usgs.gov/mapper/index.html