Exeter is a nice city, with plenty to do. The Cathedral is always nice to see, if only the façade. But do check out what is going on in Holy week before heading off to see it:
Herbie's is a lovely vegetarian restaurant at 15 North Street. They do fantastic salads, bean burgers, organic juice and wine and falafel. Very nice for a quick lunch.
Strada is a nice chain place, doing Itlaian stuff and very good pizzas. You can find it at the Princesshay complex, on Bedford Street. There are loads of chain type places around here, too, including Nando's and the like:
If you're looking for something a bit 'special', Michael Caines cooks at The Royal Clarence Hotel at Cathedral Yard. I've not eaten there myself, but Caines is a respected chef. You would need to book there, I'd think.
As for stuff to do...
If you have a car available to you, you could perhaps head out to the National Trust's Killerton House:
The house is, I gather, a bit boring, but the grounds are lovely for a leisurely stroll.
There is some information about Easter events in and around Exeter here:
You might like to go by train or car to Exmouth, the nearest 'seaside resort', which is a minutes on the train from Exeter Central station and has a busy, pleasant beach.
The North coast is also easily reached by train, from Central or St. David's and you could visit Barnstaple and hire bikes and head out on the Tarka trail to Instow or Braunton.
Hope you have a great time when you visit and that helps out a little bit!