Great food can be found all over the island however Palma will have the greatest concentration. Palma however doesn't have the best beach and access is gained across a busy road, I wouldn't consider a stay in Palma a relaxing one.
What constitutes a good beach for you? Mallorca has a great variety of beaches, from seculed rocky coves flanked by pine clad cliffs, resort filled sandy bays with plenty of watersports, beach bars and restaurants, pretty little fishing villages with small, quiet beaches to superb nature reserves with vast sand flats and clear blue water and no or very few amenities?
There are so many hotels, resorts and rental apartments that it's impossible to provide any comprehensive recommendation. We have been visiting for many years however we 'own' two weeks at the Marriott Vacation Club timeshare resort in Llucmajor which provides us with a two bedroom villa complete with separate kitchen, lounge, garden and 'private' pools per 8 villas along with all the expected ameniities at the central clubhouse. It's ideal for us with children and nowhere on the island is more than 1 1/2 hours drive away. It's not on the beach, the closest best beach, Es Trenc is a 20 minute drive away however there are many beautiful coves and bays along that stretch of the coast with a plethora of accommodation, some luxury five star resorts down to basic hotel accommodation.
The only places I would recommend avoiding are Magaluf (think thousands of British tourists, mainly late teens/early twenties, trawling through the bars at night getting as drunk as possible before keeling over in a puddle of their own vomit and sometimes worse) and S'Arenal (the German equivalent of Magaluf).
This is a good website although it does gloss over some of the less favourable parts of the island so use it as a guide and if you identify somewhere of interest then do a bit more research https://www.abc-mallorca.com