Yup, that's a tram stop. Served by three tram lines, each of which runs every eight minutes. Most Zurich trams run every 6-8 minutes (except late evenings and weekends) so if you do miss a connection it's not the end of the world.

Römerhof is 5 minutes from Bellevue or Stadelhofen, 9 minutes from the main station, 11 minutes from Paradeplatz... basically you can live anywhere you want so long as it's not clear out the other end of town (e.g. Höngg or Altstetten.)
I'd suggest looking out toward Hirslanden and Witikon - rents get cheaper the further you go from downtown.

I'm merging this with the "Where to live in Zurich" thread... have a look at the first couple pages for some good characterizations of the different areas.