There are some small offices available both in Portsmouth & in the surrounding towns. There is a link below that will bring up more than a dozen for you to take a look at! Please dont hesitate to let me know if you have any questions!
Our office is located in Downtown Portsmouth and this is a question that we get quite frequently regarding rentals. Similar to the real estate market in this area the rental market is very warm also, especially in the walk to Downtown market. In most cases rentals are going to be more expensive or right on par with what you would pay for a mortgage on the same property, of course depending on the down payment.
Currently in our MLS for rentals there is only 1 that would match what you are looking for which is a 1 bedroom on Merrimac St that is renting for $1250, if you would like more information on this my contact info is below.
At the end of the day for this type of rental your best bet is going to be Craigslist as most landlords can post their rental on there and have 10 people lined up to rent it, so the landlord doesn't really have the need to get a real estate agent involved to advertise their rentals.
Hope this helps.
Great Island Realty