Hard to think of any that aren't scenic. But, here are some good ones:
1. Fins 'n' things, South side of road. Great scenery - thrilling for first offroading of your new jeep. A great way to get a feel for what your jeep can do. Also pretty short, so you can do it in an hour or two, depending on how much time you spend taking pictures.
2. Long Canyon - easy and great views. (Don't do this if it's raining or has recently rained.) Start at the bottom. When you get to the top you may as well go to Dead Horse Point and Island in the Sky viewpoints.
3. Behind the Rocks road out to Pritchett Arch.
4. Hurrah Pass/Chicken Corners - another easy one.
5. Elephant Hill - takes all day to get there, do the loop, and come back, so start early. Also - fill up with gas before you go. For scenery, this is absolutely amazing. I prefer adding the extension South to hike the Joint Trail into Chesler Park, and across Chesler Park to Elephant Canyon - even up to Druid Arch if you have time. Depending on time, you may also be able to make it to the Confluence Overlook. I usually find we only have time to go to Chesler Park, or the Confluence overlook - not both. If you camped down there somewhere and got an early start you'd have more time.
I should also add - make sure you're prepared to deal with being stuck/stranded out there. If you're in good shape, you could walk out of any of these (may be a long walk though). Carry plenty of extra water, some food, maybe a sleeping bag in case you have to spend the night. Shovel, flashlight, basic tools. A small compressor so that you can deflate/re-inflate tires is also a good idea. A camelbak full of water and snacks is great for the hikes you might do, and for hiking out for help, if necessary. If you go on your own, you're taking a risk - just be aware of it and be prepared to deal with it.
In May you are likely to see several other vehicles on all these trails, although it may be several hours between them if you're out to Pritchett Arch or the Elephant Hill loop.