Second this - and just to be more specific for OP, the events you'll want to be on the lookout for are at the XL Center - street parking will be impossible then, but there's several garages in addition to the excess of lots so it's not really a challenge - especially since you recognize that parking having a cost commensurate to its demand is actually perfectly logical.

Besides that, street parking is easy enough to find, it's not really worth pointing out specific areas, and worst case scenario, the next block you go down will have a lot and/or garage if you happen to get unlucky that day.

Just to add something to consider, the bus system in and immediately around Hartford is pretty decent and since UCONN Health is a pretty big employer, there's solid transit accessibility to/from there and Hartford. You'll be looking at routes 66 and 121; 66 is a local bus and the 121 is a CTfastrak route, which is the state's only Bus Rapid Transit - think a mix of a bus and light rail. Both go through West Hartford too so they're options whether you live downtown or elsewhere in Hartford/West Hartford and want to avoid the driving commute or at least give yourself options.