Obviously in an area as large as this I have not seen everything and there may be other places as good as those mentioned.
There are some fine little places here and, at the risk of attracting hate mail, I will hazard the guess that at least two of them are even more popular than Worcester itself.
The first is the village of Broadway, one of the most popular villages for coach parties in England away from the coast. It is certainly a lovely stereotypical village full of the sort of buildings that the English still like to think of as typically English. There is a tower above the village, an 18th century folly which was later the centre of the Arts and Crafts movement. It is now the centre of a country park. I cannot comment on how many counties can be seen from it [14 is claimed] but it does provide a fine view.
The other ultrapopular spot is Bewdley, not only a very lovely town in its own right but also providing a terminus for the Severn Valley Railway to Bridgenorth in Shropshire.
AS for Worcester, I have covered its cathedral and mentioned its terrific cricket ground on another page. In addition the Royal Worcester Porcelain Works merit mention as the home of England's oldest firm in continuous production in the industry and the site of a splendid museum. The other thing in the city worth mentioning is the Commanderie, a lovely Tudor building used later by Charles the Second in his unsuccessful final battle in the Civil War.
Further south Pershore has retained the abbey church though the rest of the abbey was 'dissolved'. This is a building worth a visit.
Then there is the place seen by every traveller on the M5 [unless there is bad mist]. This is the lovely Malvern Hills where you can get near the top by car if you want and walk amid scenery which is deemed to be typically English [though I do not find it like any other bit of England] and which is full of paths for easy walking with long range views. Elgar is said to have enjoyed walking here. Many less famous people certainly have. In Malvern itself the church has a very large collection of over 1000 mediaeval tiles.
In conclusion I can say that my principal reason for visiting Worcestershire [as opposed to passing through] has been its facilities for apple and plum picking. This mixes an activity which is pleasant in itself with thrift and some fine fruit! The area around Pershore and Evesham is also reputed for summer fruits, vegetables and flowers.