Ideally, we would like to see both Arches and Canyonlands. I am looking for suggestions on good destinations within a day's hiking distance. Long hikes - 10-15 miles round trip or so - are OK. Also, any advice on a good, strategically-located spot to set up base camp would be really appreciated. I know that Willow Flat Campground in the Island in the Sky area of Canyonlands is one option, but perhaps there are better ones someone can recommend?
Recommended base camp would depend on what kind of vehicle you have. If you have a 2wd car, Willow Flats is OK, but I would recommend Squaw Flat (or Needles Oupost if full) in the Needles District as being the best trail hiking area for Canyonlands.
If you want to stick to trails, here are the best ones in Canyonlands IMHO (* indicates 4wd needed, the rest are easily passable by 2wd's). I've spent decades exploring the area, so there is a lot more to see than the ones below, but these are my picks of the best.
Island in the SkyWhite Rim Overlook
Grand View Overlook
Upheaval Dome
Fort Bottom*
Lathrop Trail
NeedlesUpper Salt Creek
Druid Arch
Chessler Park
Joint Trail
Davis Canyon* (some trails exist, but are not marked)
Lavender Canyon* (some trails exist, but are not marked)
ArchesDevils Garden/Primitive Loop
Marching Men/Tower Arch
Eye of the Whale* (short)
North Window/South Window/Double Arch (short)
Sand Dune and Broken Arches (short)
Fiery Furnace (permit required)
Delicate Arch
If you like off-trail routes, here are some of the best ones:
Island in the SkyMonument Basin* (best of the best in the Island in the Sky)
Steer Mesa
Junction Butte (shorter with 4wd, but doable from Grandview Point)
Musselman Canyon*
Confluence Overlook via White Crack*
Holeman Slot Canyon* (short)
NeedlesDavis Canyon to Horse Canyon*
Big Pocket
Lavender Canyon exploration*
ArchesUpper and Lower Courthouse Wash
Ring Arch
Lower Salt Wash
Klondike Bluffs
The Maze is also part of Canyonlands National Park, but it's also quite a ways from Moab, so I didn;t list my favorites there.
Outside the National Parks and in the Moab/Canyonlands area, here are my picks for the top hikes:
Fisher Towers
Onion Creek
Professor Creek
Corona/Bowtie Arches
Behind the Rocks/Pool Arch
Trough Spring Canyon
Harts Draw
As far as crowds go, some trails can be crowded in March (especially Delicate Arch, Devils Garden and the short ones in Arches NP and Fisher Towers plus Corona/Bowtie Arch), but the area is big enough that you can always find solitude. Most of the trails outside the ones mentioned shouldn't be that crowded. The other trails might have some people, but usually aren't that crowded. Chances are on the off trail routes mentioned, you probably won't see anyone.
The NPS official trails are mostly pretty short, and you can do all of them in the Island district within a half day or so
Round trip distances for NPS official Island in the Sky Trails:
Neck Spring Trail = 5 miles
Lathrop Trail = 10 miles
Mesa Arch = 0.5 miles
Aztec Butte = 1.5 miles
Wilite Trail = 10 miles
Alcove Spring Trail = 10 miles
Whale Rock = 1 mile
Syncline Loop = 8 miles
Uheaval Dome Overlook = 1 mile
Upheaval Canyon Trail = 6 miles
Moses Trail = 2 miles
Murphy Wash/Hogback Trails = 10 miles
MurphyPoint = 4 miles
Gooseberry Trail = 6 miles
White Rim Overlook = 1.5 miles
Grand View Trail = 2 miles
Fort Bottom Trail = 2 miles
Gooseneck Trail = 1 mile
You can hike 81.5 miles in half a day? Wow; that's pretty impressive.
There's also the Grandview to Monument Basin Trail which adds another 8, but the NPS doesn't like to advertise it.