Hi DJC...
Yes, there is a museum in Barcelona where you can see the excavated remains of the original Roman settlement of Barcino. It's in the Plaça del Rei, not too far from the Cathedral, and it's called the Museu d'Historia de la Ciutat.
You can get more information from the museum's
website . Although you do have to use your imagination a little to picture just how the ruins originally might have looked, it really does bring home just how ancient the city really is.
Hope this helps...
-greg