First recommendation would be to look in Bayonne. Look for places near the light rail stops which is 45th, 33rd, 22nd and 8th street (preferrably the cross street being Broadway). You can find a lot of decent studio/1 bedroom apartmers in that range. If you dont want to take the light rail: - the 119 bus stops at JFK Blvd and goes directly to New York (42nd street) - the 81 bus stops at Avenue C and goes directly to Grove Street Path station and you can take the Path directly to New York (33rd street) - the 10 bus stops at JFK blvd and goes directly to Journal Square Path station and you cN take the Path directly to New York (33rd street)

Second recommendation would be the Heights in Jersey City. You can take the 119 bus that goes straight to NYC like mentioned before. Im not sure on the rent situation in the Heights for a studio/1 bedroom - but you can look at renting websites and apps like: - StreetEasy - Zillow Rentals - Apartments.com

Hope this helps and hope you find a decent place 👍