Hello Vickianne. This is just a suggestion passing on my own personal preferences. Balıkesir is a transport hub but not really a tourist destination so the choice of decent hotels is very limited.
If I were travelling from İstanbul to Bodrum, I would drive another 80 kms and stay in the coastal town of Ayvalık, where there is an excellent choice of accommodation options Trip Advisor, Ayvalik
I would then continue on what I consider the more interesting route via Bergama, Meneman and İzmir, taking the excellent city ring road if you're pushed for time and joining the 0.32 Motorway in the direction of Aydın but leaving it at the clearly marked Bodrum junction. You then travel to your final destination via Söke and Milas.
This is just my personal choice of route. Please let me know if you require any more information - and I wish you pleasant and safe journeys.