Furnished Apartments For Rent In Morristown Tnnt In Morristown . When you rent an apartment in morristown, you can expect to pay as little as. See all 62 apartments in morristown, in currently available for rent. The Villas at Carlyle Place Carlyle Construction and Rentals from www.carlyleliving.net 6 days + 23 hours ago in listanza. The average home rent in morristown is $1,337. Morristown single family homes for sale;