The quickest, most foolproof cure for loneliness, homesickness, and even boredom I know is the one my very wise mother taught me long ago, and I taught it to my children, too: find someone to help.
Sometimes having a fun, self-indulgent day does work, and I'm not saying not to do it. But in my experience, volunteering or doing something for someone who needs it works 100% of the time.
And not because it makes you feel noble or something -- I think it's probably effective mostly because it instantly takes my focus off of myself, gets me out of the house, and keeps me busy instead of brooding. Maybe also because unlike a purely fun plan, there's no risk of my feeling like, "Gosh, I thought this was going to be as fun as [whatever it is I wish I were doing], but somehow it just isn't doing it for me."
Anyway, it really does work for us, so maybe give it a try. You probably will have time to do something that's a fun treat, too.