I live in Suffolk, so I reckon that I know a thing or two about East Anglia.
The first thing to say is that, for an initial visit, it might be best to concentrate on a particular
part of East Anglia, as the area is bigger than some people seem to allow for. (It's a two-hour drive from Cromer to Cambridge and even longer from Hunstanton to Colchester). However I'll try to cover some of the best bits across the whole of the region.
Many people regard the coast as the real gem of East Anglia, with many Sunday supplement writers declaring Southwold to be the finest seaside resort in the country. It's rather upmarket (with beach huts priced at £150,000 and a tiny terraced house anywhere near to the seafront costing over a million pounds) but it's still unpretentious, unlike it's snooty neighbour, Aldeburgh. It's extremely attractive, with lots of independent shops, superb Adnam's pubs and lovely restaurants.
https://www.thesuffolkcoast.co.uk/suffolk-coast-towns-and-villages/southwold
http://www.visitsouthwold.co.uk/
The North Norfolk coast is also deservedly popular, with Wells-next-the-Sea probably being my own favourite place. It's a delightful town, with a bustling working quayside and lots of (often upmarket) independent shops. It's also packed with good pubs and restaurants. (When I had to decide where to go on my birthday this year it was Wells-next-the-Sea that I headed for. It's impossible to have a bad day there).
https://www.visitnorthnorfolk.com/places/wells-next-the-sea-holkham.aspx
https://www.wells-guide.co.uk/
There are other interesting towns on the North Norfolk coast too, such as Sheringham.
http://visitsheringham.co.uk/
Coming inland, the best town or city has to be Norwich. It's packed with historical attractions, great pubs and restaurants, several good theatres, etc.
https://www.visitnorwich.co.uk/
If you were looking for a smaller town to visit in Norfolk then Holt should be near to the top of your list; it's absolutely charming.
http://www.tournorfolk.co.uk/holt.html
Suffolk's most popular tourist town has to be Bury St Edmunds, which is attractive and fairly upmarket.
https://www.visit-burystedmunds.co.uk/
However Ipswich has re-invented itself over the past few decades and, far from being the drab, boring place it was when I was brought up there, now has a lot going for it. In particular the redeveloped Waterfront area is now very attractive and packed with good bars and restaurants.
https://allaboutipswich.com/
If it's picture postcard places in Suffolk that you're looking for though, Lavenham ought to be top of your list.
http://www.visit-lavenham.co.uk/
Cambridge is, of course, world famous for its history and its colleges but the city centre itself doesn't immediately leap out at me and shout about it's attractiveness. It's a city where you have to do your research first, before visiting, to ensure that you discover all of its gems (of which there are many).
https://www.visitcambridge.org/
Those are just the first few places which come to mind. If you tell us about any special interest you might have (museums, bird-watching, theatres, etc) I might be able to be more specific with my suggestions.