Can anyone recommend the nearest hotels to this station
Hi Stefanie. I do not know what type of hotel you are seeking, but the Premier Inn, Portsmouth City Centre is directly next to the Station. Here is the link to the official site and you will see in the main image the station to the left. There are other hotel quite near like the Ibis. These hotels all also appear on the usual booking sites so you can obtain comparative prices and check out reviews.
Yes Premier Inn is the closest. I have also stayed at Travel Lodge and Hotel Ibis on good deals but they are a further walk away. You can also look on Google Maps for B&Bs.