I found this company in Yogya that does day tours:

http://www.viaviajogja.com/index.php

They are the ones who quoted me the car cost only for the suggested 4 day tour. I'm thinking maybe I should have some ideas of what I want to do in mind, and then book the day trips when I get to the hotel in Yogya. The only trip to book in advance would be to Borobudur to stay at the Manohara Hotel the first night per your suggestion for day 1. This is the current cost:
Double Room
6 m X 3 m X 2,65 m
1 Queen Size Bed ( 2 m X 1,6 m )
IDR 745.000 nett/room/night include
Inclusive:
Borobudur Entrance (06.00 am up to 05.00 pm)
Breakfast (American, Continental or Indonesian)
Welcome drink
Tax and service charges
Sunrise Tour
In house guest (who staying at Manohara): IDR 230.000 per person ($24)

So $77 a night with breakfast and entry to Borobudur included, except the sunrise charge. I'd probably forgo that and enter at 6:00am, just after sunrise but before the day trippers get there. And another entrance the afternoon of our arrival. I can hire a guide at the temple for one of the days.
I'm sure they hang around the entrance offering their services.

In looking at a map of the area Borobudur is half way to the Dieng Plateau. maybe I can go there for the day before heading back to Yogyakarta. I might be able to find a 2 day tour from one company that has Borobudur and Dieng all for one price.

After hanging out in Yogya for a few days, including day trip to Prambanan, we could do a tour to Candi Sukuh and Cetho, then overnight in Solo. Tour Solo the next morning then head back to Yogya. The Mt. Lawu temples and Solo look to be in the same area.

Looks like I have much more researching to do. But I like your suggestions jiejie. Stay indoors in Beijing-I saw the articles about the air pollution. And I thouht it was bad when we visited October 2011.