A few honest notes
The İstanbul night Marriott has no hotel in Kadıköy itself, and its nearest central Asian-side properties — the Sheraton Grand and Marriott Asia in Ataşehir — run roughly $200–260 in late August. So this one night trades the $150 cap for a genuinely central base near the fast train. If the rate stings, two fallbacks: the Istanbul Marriott Hotel Pendik is around $95 but sits out by the airport, or Moxy İstanbul Taksim is under budget on the European side, about 25 minutes from Söğütlüçeşme on the Marmaray.
Booking Ankara and İzmir both sit comfortably under $150 at typical rates, but confirm on Marriott Bonvoy for your exact dates — and if one creeps up, there are other Four Points, Moxy, AC and Courtyard properties in each city to swap in.
Ephesus? İzmir's famous neighbour, Ephesus, sits about 75 km away — outside your "nothing far, no day trips" rule, so it's left off on purpose. Ancient Smyrna's agora, Kadifekale and the museums give you the archaeology fix without leaving town.
İstanbul is a single arrival night, so it stays deliberately light — Kadıköy and the Moda shore are enough for one evening. If you ever add a night on the front end, the historic peninsula is a 20-minute ferry across the water: Hagia Sophia, the Blue Mosque, Topkapı and the Grand Bazaar, all within a walk of each other.
Trains Book the YHT a few days ahead on the TCDD site or app. Note that not every Ankara train calls at Söğütlüçeşme — some start from Pendik — so filter for a Söğütlüçeşme departure when you book, and pick a mid-morning one that suits a relaxed checkout.