Here are a few sources I found, in order from most user-friendly to most technical.
iNaturalist has data about where fish were actually observed. Anyone can post geo-located pictures of organisms they've observed and get help identifying them. They currently have 2,475 observations of fish in New York state, which unfortunately is a little sparse. You can see those observations distributed on a map, and filter them by species or date. It's a good way to see what people people near you have caught recently.
An old-fashioned field guide can be a great resource. Atlas of Inland Fishes of New York is available as a pdf file for free from the New York State Museum. It has 179 species distribution maps. You can also view the maps on the DEC website, Fish Atlas Maps of New York.
This resource doesn't have the "two-way mapping" feature you wanted, but if you can find the source data that was used to make the species maps you could use it that way.
The New York Department of Environmental Conservation has information about where to fish for a few major species:
They also conduct surveys of where fish are being caught. Summaries of those reports are here.
Various datasets are available through data.ny.gov, for example:
The Division of Water conducts aquatic biological monitoring at specific locations throughout the state for
benthic macroinvertebrates, field chemistry, and at some locations, sediment, fish or diatoms
I was able to find the sampling locations on data.ny.gov, but not the actual fish sampling data. However, if you request it they will probably provide that data to you. There's a link to contact the dataset owner on the dataset page, or you can contact the Bureau of Fisheries from the contact info on this page. (I have made similar requests for fish sampling data from the Ohio EPA. They were happy to email me the data I requested.)
There's a link on the sidebar of the Fish Atlas Maps of New York to a website called FishBase. It's basically a crude interface for a worldwide database of fish data, including distribution maps for hundreds of freshwater species. I haven't fully looked into it, but there might be an enormous amount of useful information there.