Best time to visit in Java is during dry season that it is more convenience to explore the area either for natural or cultural attractions in Java. Dry season usually starts from April to September.
Peak season in Java is during Idul Fitri Holiday period, this means D-7 till D+7 period. As majority of people in Java are moslem, the price for transportation, driver, hotel are more expensive during this period. Cost of transportation and hotel will rise up to 50%-120%, and guide service will be double price than normal season or 100-130%. If you want to avoid this, you can check first Indonesia calendar or ask tour operator about this. During Idul Fitri period is when locals return to their hometown to celebrate, that the traffic can be unpredictable. And also when Indonesians visiting some places of interests in their own country.
And other peak season is in the Christmas and New Year Period. As in other areas, hotels in Java also apply compulsory dinner on Xmas/New Year eve and guest may not check out on the 31 December. You can check to your hotel regarding this to anticipate any cost for your travel.
On Idul Fitri period, usually train ticket and flight will be fully booked. If you really want to travel to Java during peak season, recommended to book at least 2 months in advance. Some tour operators does not arrange tours on the peak season period.
If you are on a good budget, it will be no problem, but if you are on a tight one, you must be really careful to manage your convenience to travel. To get the most of what you pay for, you can book tours with driver only, without tour guide enroute, yet local guide for some a little difficult activities like hiking can be included. However for your information, in Jawa, there is very limited number of English Speaking Driver. Driver usually knows a little English and however they often go on such tours though. If there is train available connecting some destinations/cities, ask tour operator to connect your trip with train, for example to/from cities like :Yogyakarta/ Surabaya/Probolinggo/Banyuwangi/Bandung/Jakarta.
Not just traffic, some natural and cultural attractions will be more crowded as well with domestic tourists. For example, Mount Penanjakan Bromo will be full of tourist, that usually tour operator will recommend other view point with less people. And due to the limited number of hotels in some locations, especially at Mount Bromo, Wonosobo, Lumajang, better book in advance to make sure you will stay in a decent one with a good location.