The city centre was Portsmouth's main shopping centre until the development of Gunwharf Quays. There are a few student accommodation options in the city centre and they're usually on the expensive side. However, you get to have the University of Portsmouth campus and the clubs on your doorstep.
See all properties in the City Centre neighbourhood
Images courtesy of: Flickr under the Creative Commons License, "ExPERT centre in james watson west" (CC BY-ND 2.0) by jon crel, "Bus alley surrounded by shops" (CC BY 2.0) by Matty Ring, Stuart Cann [CC BY-SA 2.0], via Wikimedia Commons, By Ahmed Al-Iessa (Own work) [CC BY-SA 3.0], via Wikimedia Commons