The weather has been raised as a factor in favour of Brighton as compared to Edinburgh. If you compare the official weather data you will see that average annual rainfall and number of rainy days is about 30% lower in Edinburgh (450mm/yr) compared to Brighton (650mm/yr). Brighton is not only wetter but also more windy than Edinburgh. By contrast, Brighton is a little warmer. Mean daily January and July temperatures are 3 and 14.5C for Edinburgh compared to 6 and 19C for Brighton.

For me Brighton is a party town and a good gay dormitory for London but not much more. The beach is nothing to write home about, I would prefer to jump on a cheap flight from LGW and go to Greece or Canaries for a few days. Brighton lacks the soul, character and atmosphere that Edinburgh has in abundance. Also, in terms of other visiting/sightseeing opportunities Edinburgh wins hands down with day trips as diverse and far afield as Loch Ness in North and York in the South being a possibility. If you are attracted to outdoors or winter sports such as skiing or boarding then Edinburgh comes out on top again given it's proximity to the resorts in the North.

While I personally love London I note your original post so do not advocate it as some others have. Somebody suggested Bath; I have no idea what the gay scene is like there but the city is gorgeous and I imagine a nice place to live and work.