One of the ornate entry signs to the Batik Kampung
While people flock to Yogya to buy batik from the stalls lining Malioboro street, Solo has its own big batik production facility (and probably makes most of the stuff sold in Yogya). The main batik 'market' in Solo is actually a maze of narrow streets near the Kasunanan Palace called Kampung Batik, or the 'batik village'. Unlike the crowded stalls of Yogya, the batik village is rather sedate, with over 40 shops and boutiques to browse through. It's a hodge podge of buildings, some of which date back to colonial times, so it can be an interesting place for a stroll even if you're not buying anything.
For more background on the area and the history of batik in Solo, there's a good article on the Solo city government web site.