You’re overthinking this. Hire a driver on 2-3 of the 4 days to drive you to places. The rate is $35 for 10 hours. The two coolest temples you want to do are Tanah Lot and Uluwatu, so staying somewhere between them is a good choice. But anywhere around the broader airport area is central enough. The intercontinental is a pretty resort, on the beach, and in a decent price. A lot of the hotels in Bali are either not on the beach, or the beach is not that good, or they are more isolated, or they are run down, or they are too expensive. The intercontinental avoids all these problems, IMO.

John Wick may also be there, or at least his cute dog, so you may also get to meet celebrities ...

hotels in the seminyak area area maybe more walkable close to town, as opposed to more isolated resorts, but I am not sure, and hotels or the area may not be that pretty. Taxis and grabs are very cheap though and preferred for transport anyway, as it will be hot and humid. Or best to have the driver drive you everywhere and wait for you...