honestly, closest to where that hotel is? Giant Eagle on Britton Parkway. Go north on 270 one exit...Cemetery Rd westbound. Turn right on Britton parkway. It's a big chain grocer, but has a really nice beer selection.
Gentile's on King Ave is about 10-15 minutes away but may be the closest with a wider selection than Giant Eagle, which is pretty good
Less than a 20 minute drive to the Andersons on Sawmill (7000 Bent Tree Blvd), which is one of the best selections in the city, as well as less than 20 minutes to The Daily Growler on the corner of Fishinger and Riverside (2814 Fishinger Rd), and The Ohio Taproom in Grandview Heights on the corner of Northwest Blvd. and 3rd Ave (1291 W 3rd Ave). Both of those do growlers (Ohio Taproom does counterpressure filling using the Pegas CrafTap system and also carries some bottles/cans). Also, I second Gentile's, they have a good selection, as does the Market District Giant Eagle (which is just down the street from Ohio Taproom on 3rd Ave). Cheers!