I asked Nashville visitors where they stay when they want to be close to Broadway, and one hotel came up again and again in the responses.

Drury Plaza Hotel
The Drury is hands-down the most recommended hotel for staying near Broadway. It's about two blocks from all the action, which means an easy walk to the honky-tonks without being right on top of the noise.
What makes the Drury stand out? The free breakfast buffet and happy hour with drinks and food are huge perks. There's a heated rooftop pool and hot tub where you can unwind after a day of exploring. The beds are comfortable, and recent guests say they had zero complaints about their stays.
<– CHECK PRICES & AVAILABILITY –>

Downtown Hilton
The Downtown Hilton on 4th Street gets a lot of love from repeat visitors. It's the closest hotel to Broadway, which is perfect if you want to stumble back to your room without much of a walk. Multiple people mentioned this as their go-to choice.
<– CHECK PRICES & AVAILABILITY –>

Margaritaville Hotel
If you want to be right in the thick of things, Margaritaville sits directly on Broadway. You'll have live music literally outside your window, so keep that in mind if you're a light sleeper. But for some people, that's exactly the experience they're after.
<– CHECK PRICES & AVAILABILITY –>

Omni Nashville Hotel
The Omni came up several times as a solid pick near Broadway. It's a bigger hotel with all the amenities you'd expect, and the location puts you close enough to walk to the action.
<– CHECK PRICES & AVAILABILITY –>

Moxy Hotel
The Moxy is right across from Posty's and next to Kid Rock's bar. Fair warning — there's live music until around 4am, so you'll hear it. But if that doesn't bother you, it's got valet parking and puts you right where everything's happening.
<– CHECK PRICES & AVAILABILITY –>

Grand Hyatt Nashville
One visitor stayed at the Grand Hyatt twice this year and loved both stays. It's a reliable choice if you want a higher-end experience close to Broadway.
<– CHECK PRICES & AVAILABILITY –>
Other Options Worth Considering
The Renaissance gets mentioned as a good pick, and the JW Marriott isn't directly on Broadway but close enough to walk. The Fairlane and Embassy Suites also showed up in recommendations.
If you're watching your budget, the Holiday Inn and Comfort Inn near the stadium offer free shuttles that run all day and night. The Comfort Inn also has free parking, which is a big deal in Nashville.