There are ported subs that don't sound boomy. Like everything else in this hobby, it's all about good design. Lots of factors matter here - cabinet size, amplifier power, driver size, magnet structure, excursion, etc., etc.
In your price range, the SVS is a good suggestion, but the RELs are also a good idea. And there are others. Also, consider a sub with built in DSP or at least an adjustable node filter. That can help a lot with the boominess.
In your price range, the SVS is a good suggestion, but the RELs are also a good idea. And there are others. Also, consider a sub with built in DSP or at least an adjustable node filter. That can help a lot with the boominess.