I am local. It is a fabulous place if you like walking and coastline. If you want to be able to walk to shops/ restaurants etc, then I would stay in Mumbles. If you’d prefer rural / coastal, I would look at south Gower - Port Eynon, Horton, Oxwich all have direct access to beaches.
There are some lovely campsites with glamping options, various cabins etc on AirbandB, and holiday cottages / apartments. Home from home is a good local holiday home agent. Hotels aren’t great really - a few in Mumbles and Oxwich bay hotel and Parc le Breos on Gower but they will be expensive.
PP has already said about options in the city. As for Gower itself - the coast path goes all around Gower and it is beautiful walking. If you like surf/ body boarding , Llangennith is the best option, followed by caswell - sometimes great for surfing and other times like a millpond. Surf shops will rent boards etc - Paddle boarding is big here too. Bring a wetsuit- the sea is cold! Beaches that have parking and are good for the day - Langland and Caswell are near Mumbles and have facilities etc - busy but lovely. Oxwich/ Port Eynon/ Horton/ Llangennith all have parking and are big enough to find quiet spots.
I prefer the beaches you have to walk to, and the smaller cove beaches. So if you take the coast path from caswell, you reach a tiny bay after half a mile (Brandy Cove) and then Pwhll Ddu , which is magical. You can also reach PD from Bishopston village. Further out you have my favourite stretch - Pobbles , Three Cliffs, Tor Bau, Crawley- you have to walk to all of them. Pobbles and Three Cliffs are stunnning, amazing dunes and games on the beach but TC in particular is known for rip rides, I don’t swim there with my children. Tor Bay is sandy, great for rock scrambling and swimming and often v quiet. Crawley is a walk through woodland and again, fab dunes.
Other favourite small beaches are Mewslade (low tide only) and Fall Bay - they are both a lovely walk from Rhossli.
North Gower has incredible beaches but is more known for walking - not swimming beaches.
There is usually fruit picking at Scurlage and there is an archery centre - Perriswood.
Best places to eat are the Brittania in Llandmadoc (North Gower) and I understand that the Gower inn in Parkmill has new owners and has great reviews. Also the King Arthur in Reynoldston.
If you like Castles - Oystermouth in Mumbles - they also do some events there -music days and outdoor theatre. On Gower there is one near Llandrhidian - the name escapes me. There is also Pennard castle, v little left now , but an incredible position overlooking Three Cliffs Bay.
Gower Adventures I think it is called run RIB boat trips around the coast but they are expensive. There are lots of seals around and a colony by Worms head. - Worms head is an amazing walk - it can be challenging in parts and can only be done 2.5 hours either side of low tide. Gower has huge tidal changes so do keep a daily check of tide times.
I think that is all for now - but would totally recommend the area. I came on holiday here 22 years ago, and moved to Swansea 2 years later - I am never moving! 😂😂