I know that it's OK to say: "What lovely weather we are having today!" But if we mention the place where we are not present at the moment, can we use 'they' instead of 'we'? Or are there some other possibilities to use this pattern?
As a native American English speaker, I would understand it if you said "What lovely weather they are having in Hawaii today", as mentioned in the comments, but it would not sound natural to me. Instead I would say something like "The weather is lovely in Hawaii today".
As for the pattern, "what ____ we are having today", I can't think of another place it would be commonly used.