Rent it. If you haven't decided what to do with Grandma's house just yet, you can always rent it out for a little while. Without making substantial upgrades, you may be unable to charge premium rent.
However, if you've been considering keeping it and making it your own, the income you can get from it is still more than you'd get from leaving it empty. Call a property manager for help if you need to find good tenants and have someone handle the marketing and management.
Sell it. Many people get into huge trouble when trying to sell a house they've inherited. They either go in with a full remodel, spending tens of thousands of dollars on a house that might just as easily find a buyer in its current condition (even if the sales price is a little lower), or they contact a company that will buy the house as it sits. Both are setups for disaster.
Before you do anything, consult a few local real estate agents for advice and then do the math. What does it cost to remodel versus what you'll earn from the sale of the house? What would you walk away with if you sold the house as-is? How much is the house really worth compared to what the guy who will close in a week will give you?
