IMO get an under sink filter. I suggest either the Filtrete 3US-MAX-S01 or an Aquasana AQ-MF-1 (buy quality fittings as the kit ships with subpar ones). They essentially filter the cold water side of the faucet and remove most of the funky taste of most public water. If you are on well water, consider something more substantial but both of these will remove the nasty stuff such as lead and are relatively higher flow with affordable and simple filter changes.

Easy to install and will last years with regular filter changes every six months or so. I put our last one in twelve years ago and still going strong. The Aquasana is a better overall filter but frankly the Filtrete on public water gets the job done just as well for half the price.