The best reason to time a visit to Erlangen specifically is the Bergkirchweih, which runs for eleven days in late May and early June. It is one of the most authentic folk festivals in Germany and coincides with pleasant spring weather. Accommodation fills up fast during the festival — book ahead if this is your plan.
The rest of the year, Erlangen is pleasant in all seasons. Summer is warm and the Schlossgarten and Botanical Garden are enjoyable. The Christmas market in the Altstadt in December is smaller and less touristy than those in Nuremberg and Bamberg, which can be a point in its favour.