Hi,
If I was you I would get the train from Semerang to Surabaya. Stay the night - nice old hotel is the Paveljohn, and next morning get the train at about 9am to Probolinngo railway station. Good idea to book bisnis or eskutif class the day before.
From there get a local bus to the bus terminal in Probolinggo and get a bus up to Cemoro Lawang. Do not be talked into getting a tourist bus- it simply does not exist- just another way of separating you from your money.
If you stay in Cemoro Lawang at Lava Cafe, you can book a jeep for about 50,000 rupiah at the cafe next door with other travellers for a 5.30 am start to see the sun rise. You go up to the viewing platform to see the wonderful Gunung Bromo and all the surrounding mountains.
My photos of Bromo
http://travel.webshots.com/album/556530994AliQiYThen from Cemoro Lawang get a bus back down to Probolinggo and then a long bus ride to Yogjakarta to see the Borobudur, Prambanan and possibly a trip to Dieng Plateau.
How long are you planning on staying in Indonesia? If you need to have a visa to enter Indonesia do know you can only get 30 day visa on arrival. Any longer and you need to apply at the Indonesian Consulate in your home country or in one of the Asian cities like Bangkok, Kuala Lumpur, Penang or Singapore.
Pamela.