You might re ask your question with a few towns mentioned so that agents in those towns can respond.
By the way, there are 16 rentals in MLS in Charlestown.
The least expensive is listed by Century 21 Elite Realty (617) 241-5566 List Agent: Jennifer Schneider.
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This rental has issues. It shows that it is in Charlestown, but it isn't. It has East Boston schools associated with it but the listing says it's in Haverhill.
If you are interested in Charlestown, Boston, Cambridge, etc...then I can help, but if you are interested in the North Shore areas, then I can recommend an agent to help you. The rental price of $1200+ is not available in Charlestown.