Logan Airport is right next to the city. It is easily reachable by car, public transport, or taxi. More information is available at the airport website.
You can take MBTA buses and trains anywhere in Boston. You can take the Silver Line bus from the airport, but use Apple or Google Maps to find the best route for your time of day.
Boston has a large range of hotels to choose from. We have some suggestions but you will have no problem finding a hotel to suit your preferences.