That's a good question. The parking around the Capital is street parking and garages, I found metered parking a few hundred yards from the Capital. However that's a fairly busy street. City Island might be possible if the Senators aren't home. However you'll have a little walk from City Island to the Capital so if it's raining or extremely hot that might not be the best.
The City Island has free parking lots if no special events are held.
Goodluck theres a bunch of small streets. Best bet is to go and park after 5pm when it's free parking other than that it's hard to find any parking. As its meter and permit parking.
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