I see a few in NJ over 5%: MUJ, MYJ, NXJ. NXJ is at a 10% discount. I've been basically doing those Nuveen & Blackrock equivalents in CA.
I usually go for discount to net asset value so I feel like it has room to appreciate so I can lock in a gain outside of the monthly dividends. And if they go down you can always scoop up more which will then have a higher annual dividend yield.
They are state tax free if they are issued in the state you live in. If they are federally tax free, they are tax free in any state. Be aware that not all MUNIs are federally tax free.
You would not get the state tax free benefit of a California bond if you live in New Jersey. But you would get the federal tax free portion.
I suggest that you confirm with your brokerage's fixed income team before proceeding.
The reason I ask is because I can't seem to find any NJ municipal bonds that are providing a 5% yield. They all seem to be around 3%.