There are several hotels in the city. But you have to be careful with them. The city is famous for having a lot of prostitution and you can end in a hotel that is used for it.
It´s safer to use hotels that are big. The may be a little more expensive than others, but you won't get ruined. Some of them are:
You can also hospedate in Hotel del Norte. Is a beautiful hotel that is more than 100 years old. Is in the old downtown of Puerto Barrios and is close to the City Hall and the Central Market. But it is close to the port, so there's a lot of traffic and dust.