That shouldn't be a bad walk to the stadium and there's some good bars and taprooms west of there as you head into Grandview on 5th Ave. You should see more of the working age, 20-40 somethings out there vs. the closest options on High Street.
High Street should be divided into sections. North of Lane Ave you get into Clintonville. I haven't been out much in this area but it's been a hot neighborhood for a number of years and there's a lot of highly reviewed bars/restaurants, but it's getting to be farther away from everything else.
South of Lane Ave down to 10th and 11th Ave is going to skew younger and students as it's on/adjacent to campus. It's fun (and more diverse, age wise) on game day, but it's going to be crowded.
South of 5th Ave you get into the Short North, and that leads to the Area District and downtown. There's a ton this way and it can be a very mixed and eclectic crowd, depending on where you actually go. If you want options, this is probably your best bet. None of it should be more than a 5-10 minute ride from where you're staying right now.