Rafa Esteve, CC BY-SA 4.0
Just an hour down the coast from Barcelona is the old Roman city of Tarraco (now Tarragona) with is impressively situated amphitheatre.
Tarragona seems to effortlessly juggle being both a UNESCO-listed tourist destination and a busy port with all the associated industry.
Ancient history can feel remote from our times, and some Roman sites are a bit dry. However, here the Roman past is brought to life through the smallest (and saddest) of Tarragona's many finds. A children's doll was found in the grave of a four or five-year-old girl. The telling of this story along with all the other finds at the Archaeological Museum, makes the distant past feel much closer.
Roman Amphitheatre
Praetorium and Roman Circus
The tourist information office have come up with a series of strolls, which you can see here.
If you'd like a guided tour, here are some providers: https://www.tarragonaturisme.cat/en/activity-providers
If you are just passing through and want to drop your bags and go for a stroll, Nanny bag has a list of places you can use.
https://www.nannybag.com/en/luggage-storage
There are regular cheap local trains between Tarragona and Barcelona taking around an hour. It's also around an hour from Zaragoza and two and a half hours from Madrid, but high speed trains stop at Camp Tarragona which is 8km out of town and requires a further connection to get into the city.
In theory you could get to Tarragona from London in a day by train, but with plenty of places to hop off on the way, why not slowdown?
https://www.rome2rio.com/map/London/Tarragona#r/Train
Tourist Info: https://www.tarragonaturisme.cat/
How about Barcelona , Zaragoza or Valencia ?
Here's a link to tourist information: Tourist info website
Why not plan your own trip one hop at a time with Trip-Hop: