My primary piece of advice would be to get a hotel room if you're able to. If you're financially or otherwise unable to, spend the day before your staycation cleaning your home and hiding all signs of responsibilities. This means no bills on the table, no grocery list on the fridge, no dishes to do, etc. It might be a bit of extra work, but it'll make your weekend that much more enjoyable and relaxing.
Use this occasion as an excuse to dress up. Part of traveling is dressing to fit your new environment, so it only makes sense that you should change up your outfit selection for your staycation. It'll make you feel distanced from your everyday life, not to mention glam as hell!
If you're desperate enough for a vacation to create one without having to go anywhere, you deserve to treat yourself. Nice meals, mani/pedis, even just a day where you unplug and catch up on reading are all great ways to treat yourself to a relaxing staycation. I decided to get my eyebrows done at the Benefit Brow Bar: something I hadn't done in over a year. Check out my "after" pic and the sweet tweet I got from Benefit!
One thing my parents taught me about staycationing is that it's the perfect excuse to act like a tourist in your own city. It wasn't until I first went into the original Nordstrom that I realized I'd never actually been there in the year+ that I've lived in Seattle! I typically associate tourist activities like that with, well tourists. If the original Nordstrom store was in any other city in the world, I would make it a priority to visit on my vacation... So I did just that during my staycation.
I'm going to end this post by reiterating a very important piece of advice: avoid your responsibilities during the extent of your staycation. Just because you're still a twenty minute walk from work doesn't mean you should feel indebted to covering someone's shift; just because you're right around the corner from campus doesn't mean you should spend more time studying than necessary. After all, you wouldn't do either of these things if you were 100 miles away on an actual vacation. The only thing that differentiates a staycation from a vacation is your location; the state of mind is the same. Embrace that!