I have a database that has information such as Latitude, longitude, plus other information such as sightseeing locations, restaurants and shopping centers, if it's rural or suburb,... It also has grids and centroids for each grid on the map. I need to cluster the area based on similarities, so when someone is driving, they can visit the locations. I have also added information such as zip code and name of the city and county. What clustering algorithm or models is suggested, so that apart from similarities, it can keep closeness of grids into consideration?
Columns: Lat, Long, centroid(most populated area), restaurants, distance to restaurants, city, state, zipcode
Methods I have tried: K-means, Gaussian Mixture so far. problem with K-means is that some portion of a cluster is in one zip code, and the rest is in another zip code. I need everything in a cluster be in a similar area.
My last question is do I do normalization on latitude and longitude? thanks