There must surely be someone on the forum more knowledgeable about Naples than I am, but I'll contribute the little bit of knowledge I have, hoping it won't lead you astray.
I walked along the Via del Parco Margherita a couple of times because it has some lovely Art Nouveau/Liberty architecture. I didn't get quite as far west as the Grand Hotel Parkers. It's an upscale neighborhood but might consign you to using taxis every time you left the hotel, because it's well west of most of the city's traditional sights; the exception would be the waterfront itself, well south of the hotel. I don't remember whether you'd be going down a steep hill to the water; it's definitely steep as you walk away from the water upon leaving the hotel. There's a Metro station at Piazza Amedeo, but I don't know whether there's a way to get to it from the hotel without walking all the way around the Via del Parco Margherita loop. On a short visit, you wouldn't want to do that, I assume. It appears that line would take more time getting you to the train station and would drop you off a bit of a walk (flat or downhill, I think) from the archaeological museum. There might be good views from this hotel, and the neighborhood may well be more memorable than the one around the Romeo.
The Romeo is closer to the sightseeing center of town and a shorter walk to the Metro (Municipio Station). The Municipio Station is a useful one, getting you to the train station or the archaeological museum without needing to transfer. I didn't walk through the area right around the Romeo, so I can't tell you anything about the neighborhood. I think this location may put you near a less attractive part of the Naples waterfront, but I'm not sure.
If you want to see the Veiled Christ statue at the Capella Sansevero, get online tickets ahead of time. It sells out. The chapel is within easy walking distance (downhill) from the archaeological museum.
