The way it sounds, your tap water does not taste very good? That is unfortunate since it costs you in time and money to replace it for brewing. Looking into what your tap water quality is, may enable you to correct the tap water for brewing use. Some simple treatment may be all that is needed. But you won't know until you find out what your tap water has in it. Call the water company to see if they can provide the secondary water quality parameters we brewers are interested in or have a sample tested yourself.
The Arrowhead water may be a good alternative. But as others have pointed out, the variation in the quality noted in that report makes it difficult to plan your treatment requirements prior to brewing. I expect that the water you get at a certain store is probably from a single 'spring' source, but you never know for sure. I know that they do use multiple sources. With a single source, then you might have a better chance in obtaining a consistent quality and calibrating your brewing practices to that water.
One relatively easy way to monitor water quality is to have a total dissolved solids (TDS) meter. That way, you can quickly assess if the water's TDS is similar to the water you have been using. You won't be able to assess what the levels of the various ions are individually. But it will help point out gross changes in the water. By the way, RO water users should always have access to a TDS meter so that they can monitor the quality and performance of their machine or a commercial machine and assure that the water is reasonably 'pure'. Remember that RO water is never truly pure, just close to it.
Another somewhat quick assessment that is most important to brewing is the water alkalinity. That can be checked with a test kit. Aquarium test kits can be quite inexpensive.
With those 'tools', a brewer can manage the most important aspects of a variable water supply. Moving to a RO water source may be a good option for removing the variability concerns with a water supply. Do consider that.