The best idea is probably to rent downtown, unless you want to take a commuter train to one of the towns you're planning to visit and pick up a car there. I don't think going to the airport just to rent a car makes sense.
Are you renting the car for just a day trip, then returning to your hotel? Or planning to spend a few days outside of Boston, with the car, then return to fly home?
I agree with post #1 that it probably makes the most sense to rent downtown. If you rent from a location near South Station or Back Bay Station, it will be easy to return the car and get to the train. I suppose an alternative would be to take the commuter rail from North Station in Boston to Salem and rent there. If you return the car in Salem, you will then need to transfer from North to South Station by subway or taxi when you get back to Boston.
Are you planning on just seeing Salem or touring around other cities on the North Shore? Salem is compact & very walkable. No need for a car to see Salem, but if you want to do scenic drives you'd need a car. The commuter rail does go all the way up the coast to Gloucester, Manchester, Newburyport & Rockport.
The airport is not very far from the city. You will have many more options for rental cars at the airport. It might be cheaper to pick up at for example Alamo at the airport than Hertz downtown. It would of course be marginally more convenient to pick up near your hotel and drop the car off near the train station, but I wouldn't rule out picking up the car at Logan if that's where you see a better deal.
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