I spent a day in Izmir and I really enjoyed just walking around the city. Don't rely on Wikipedia for sightseeing ideas. There are some absolutely beautiful places to see in Izmir. If you want more ideas, get a good guidebook, or get one from the library and read up on Izmir.
I spent some time at the Agora ruins, the marketplace of ancient Smyrna. The Agora is mostly in ruins today but it was still impressive. and well worth seeing.
You could visit the gorgeous Hisar Mosque. And there is also a wonderful market called the Kemeralti Bazaar. I enjoyed walking around and seeing the various items that were for sale, and bought a few gifts to bring back. Here's an article that gives a good description of it: https://www.lonelyplanet.com/turkey/aegean-coast/izmir/attractions/kemeralti-market/a/poi-sig/1249467/360867
You can also walk down to the harbor to see the boats. I went there at sunset and it was absolutely beautiful. There are so many things to see and do. If it's a beautiful day, there's no need to spend it in a dusty museum.
There are wonderful restaurants in Izmir, too. If you haven't had pide by then (or even if you have), make sure you get some. I loved stopping for food at the street vendors, too. Izmir is really an enjoyable city - more modern than most of Turkey (and more secular) and well worth a visit.