If you stay in Dunsmuir make sure to stop at Yak's, it's the best burger joint I've ever been to.
The Lower Sac should be pretty good with some great caddis hatches. Wade fishing options in town are good and I THINK the flows are still low for most of May. They ramp up flows in the summer so make sure and check in to that.
I don't have a ton of Upper Sac experience. The McCloud is insanely beautiful but it seems to shut off every single time I approach the river. it's always "shoulda been here yesterday!!" I still highly recommend it.
If you do the Pit River, bring a buddy. Wading is really really gnarly and the hike in and out is a steep rugged canyon in a lot of places. It's not a place you want to break an ankle and get stranded. I love the Pit but I won't fish it alone.
An interesting nearby lake option in Baum Lake outside of Burney. It's a small reservoir above the famous fly fishing section of Hat Creek. It has a million cookie cutter stocked browns and bows, and also some VERY large wild rainbows and browns. In May when the weeds grow out you can stalk big cruising bows sipping callibaetis emergers. A couple years ago I fished for this cruising bow that probably went 24" for two hours, only to be foiled by a bad knot when he finally took the fly. I love Baum Lake, it's one of my favorite places.
I never fished Hat Creek very much. I know they've done a lot of restoration efforts in recent years so it's probably worth checking out.
The Fall River is cool as hell. Access is a bit limited and you can't launch a boat with a gas motor at the CalTrout access. I've only fished it during the Hex hatch and it's a lot of fun.
Looking the other direction, the Trinity will probably be crap, but Lewiston Lake can be an absolute blast. It's feast or famine there, at least in my experience. It has some wadable flats that are a lot of fun for cruising rainbows. There are also GIANT browns in Lewiston lake, I've only ever seen one, but they're in there.
The deltas in Trinity Lake (formally known as Claire Engle Lake) can be fun that time of year. I fished the mouth of Swift Creek one early June and had a really fun day catching smallmouth. One time on the Stuart Fork, I saw what I think was a huge brown chasing fish around the shallow tailout of this big pool. I didn't have a rod on me but that was fun to see.
Have a blast! That's such a cool area to fish