I live right around the corner from Lower Mystic Lake, having fished both bodies of water along with the head of the river for a number of years now, and I think that water level and temperature are two key factors in determining whether the bite is on or not.
The early-season is tough because the water temperatures take longer to warm up than other bodies of water due to the depth of the water and underwater topography, especially in the case of Upper Mystic where the depth drops off from the shoreline pretty quickly to a max of about 80 feet in the center. As a result, the water temps will take a bit longer to warm up than some other places, and due to the changes in weather in late-Spring, shoreline structure won't really begin to hold fish until more consistent, warmer weather arrives, especially in the River. In addition, the River doesn't really pick up until the water level comes up and the weed beds begin to form. This won't happen until around June 1, but it's a good time to fish, especially when there's a current in the river. The Largemouth will often park themselves on the back end of weed beds out of the current, while you can get some decent Smallmouth who are further out in the channel where the bottom is a bit rockier.
That being said, here are a few tips I'd suggest:
* If you're fishing early season I'd suggest trying the Eastern and Southern shorelines of Lower Mystic. There are a couple of places there where you have some nice flats that drop off pretty quickly, and you'll often get hits along he transition zone. I usually hit these with a weightless Senko with a slow, consistent, regular retrieve.
* The Smallmouth in the River respond pretty well to finesse worms. If you catch a day where there's no movement in the River try to scope out some of the deeper holes and drop it right on them. If the current's moving, put a split-shot on the line about 6 inches above the hook and cast upriver of the spots you want to hit, letting the current drag the worm along the bottom.
* Come mid-Summer when the lily pads are in along with the weed beds you can find some nice bass smack dab in the middle of them. For this I'd suggest a magnum worm weighted and pegged, dragging it across the pads and working it up and down in the holes; I hooked into and lost one this way two summers ago that was probably in the six pound range that I might have landed had I not been using mono. The smaller bass tend to hug the edges of the lily pads and weed beds more but are a lot of fun to catch. They tend to respond well to a quick, erratic retrieve. I've caught a couple this way using a zoom fluke in pearl that the fish have just tagged.
All that being said I think we're still a few weeks away from seeing the bite pick up. I went out on Saturday during the storms and the spawn is currently on, seeing a number of fish i shallow but not sniffing at anything I threw near them... No sign of weeds in the river or lake yet, but starting to see the lily pads come in at the southwest corner of Lower Mystic... Water level is still pretty low,but hopefully that will come up a bit... Finally, I was getting hits and landed my first bass of the year, the little Sallie seen here:
Caught him on a cut tail worm in pumpkin with black flake and had most of my hits on that over the course of about 3 hours. I lost what I think was a better Smallmouth as well but I didn't get a good hookset.
In any event, sorry for the long-winded response. There are some good fish in The Mystics and there are times when they are tough to catch, but it's not a bad bit of water to try.