The two obvious choices for a first time visit would be the Stiperstones and the Long Mynd. The greedy walker might think to amalgamate the two, but to my mind those routes that have been published trying to do this, end up missing the essence of either of these hills.
On the east side of the Long Mynd there is Little Stretton with two pubs the Rageth and the Green Dragon, the first very picturesque and antique but probably posher and the Green Dragon with a more local touch, food is excellent in both. From this start you will be able explore the batches of the Mynd. Another possibility is the Bridges at Ratlinghope, pronounced Ratchup, from this side a walk north up to Golden Valley cross east by the Portway and follow the Mynd south past Pole Bank and Pole Cottage cross west to Wentnor, where your will find the Inn on a Green, back to the Bridges about 11 miles.
The Stiperstones pub under the west side of the Stiperstones is another attractive country pub, good to catch up on the local crack there. Lovely little known valley behind the village, Myton dingle will take you up by a steeper route to the top than the normal rambler/tourist routes. If you visit the valleys behind Lord's hill and the Devil's Chair you will be putting the framework of a route together for a 10 miler, with the Nipstone and the Black Rhadley. There are the old lead mining workings of Snailbeach to visit and lot of other history to be discovered. Return to The Stiperstones for one of their excellent meals down Perkins Beach.
From these two walks your should see enough of north and south Shropshie that the is a lot more to be explored.Corndon hill and surrounds; Black Clee and Brown clee, Wenlock edge, Breiddens, Long Mountain, Wrekin, North Shropshire's chain of sandstone outcrops. North Shropshires lakes and canals. The Welsh marches secret valleys that criss cross Offa's dyke, Llanymynech's limestone and you might just stumble across the Shropshire Way that fiddle faddles around the county side stepping all the private estates and leaves an accurate record of the historic members of County Council, who did not like Clement Atlee's idea of a countryside, shared by all who defended it through two world wars.