There is no other "interesting" airport really nearby. At 172 kilometers you have the Allgäu Airport in Memmingen (FMM). This airport is sometimes called "Munich West" and served by some low-cost carriers. You have to go by bus or train from Memmingen to Nürnberg. It takes almost 4 hours. Bus prices start at 11 EUR and trains at 19 EUR (if you book early enough). Add 3 EUR for the transfer from the airport to the city.
Another interesting option can be Franz Joseph Strauss Airport (MUC), next to Munich. It's 132 kilometers from Nuremberg. It is a huge airport served by plenty of airlines. It is a bit closer to Nuremberg than Memmingen, and you have better possibilities to make the transfer by public transport. You can either take a train or a bus. A regional train costs 22 EUR and it takes 2h45 with one change. Buses are faster (< 2 hours) and probably cheaper, but less frequent than the trains.