Personally, I wouldn't spend a week in Vegas, but I see you plan to visit the GC while you're there, so fine that should keep you occupied. Red Rock Canyon is nice for a visit too and you can drive over the Hoover Dam on your way to/from GC, which is impressive.
Where else for a week? Well, what do you fancy doing? Do you want a week by the beach, relaxing, or do you want to 'do' stuff? San Francisco is lovely for a few days, but the weather can be cool and grey in the summer, so if you want hot sunshine it's a bit of a gamble. It's a lovely city though with lots to do for 3-4 days. I expect it to be busy next August though, if Brits and other Europeans are finally allowed to visit the US, so make sure you book your hotel and any attractions you want to visit in good time. You can fly back to the UK direct from SF, which is handy. You could drive there via Yosemite or Kings Canyon or Sequoia NP if you want to get some nature en route. Again, book accommodation early if you do that, because they're all likely to be really busy next August.
If you just want to relax and chill, I recommend San Diego, which also has direct flights back to London. It's a nice city with glorious beaches nearby and some nice areas like La Jolla and Coronado. There's not a huge amount to do there, maybe a couple of days' worth, but if relaxing is your main objective then it would work and the weather is reliably good.
As for Hawaii, you could go there, but it's a long way to go for a week and then you've got to get all the way home again, so I'd probably go to California.