I left Surabaya 3 years ago therefore the information may be not all up to date. I have rather vague memories about other parts of the city aside from the west. May be I'll update it next time.
Since I left, I heard about the street & park beautification, and the new city bus which you can pay the fare with empty plastic bottles.
Transportation
Angkot = angkutan kota/line/len (public transportation is not recommended) - I don't even know if they still exist.
Taxi. I only used Blue Bird or Orange.
Gojek, grab, uber.
West Surabaya
Residential area : Citraland, Graha Family, Bukit Darmo Golf, Graha Residence. They have club house & golf course. US Embassy office is inside Citraland.
School : Singapore National Academy, Surabaya European School.
Mall : Supermall, PTC, Ciputra World, Pakuwon Mall (the newest I think?), Lenmarc (quiet, not appealing). - but Lenmarc XXI cinema offers the lowest price. Surabaya Town Square lies between west & east SUB.
Stores : Hartono (electronics), ACE Hardware.
Supermarket : Hypermart. Papaya supermarket & Ranch market for imported product.
Hospital : Mitra Keluarga, National Hospital.
Some buildings for architectural sightseeing:
Hotel Majapahit. Jalan Tunjungan No. 65. There's an annual drama pictures the situation when Indonesian tore the blue part of Dutch red-white-blue flag, involving prepared Indonesian actors and accidentally-will-you-join?-foreign actors. Not sure about the date.
Kantor pos surabaya, Jalan Krembangan Barat No. 73-75
Kantor Gubernur Jawa Timur, Jalan Pahlawan No. 110
Balai Kota Surabaya, Jalan Taman Surya No. 1
Balai Pemuda, Jalan Gubernur Suryo No. 15
Gereja Santa Perawan Maria, Jalan Kepanjen No. 4-6
Gereja Katolik Hati Kudus Yesus (Katedral), Jalan Dr. Soetomo 15
Perpustakaan Bank Indonesia, Jalan Taman Mayangkara 6
Old buildings which is now a restaurant/cafe:
Society complex, Jalan Sumatera 40
de Soematra, Jalan Sumatera 75
Other sightseeing:
Tugu Pahlawan and Monumen Kapal Selam (Monkasel) - I've never been to Monkasel myself.
Sampoerna (cigarette brand) Museum.
http://houseofsampoerna.museum/e_sht_main.htm. Call to reserve a city tour.
Clubs: Hash House Harries Surabaya.
Beaches are not the one you visit to relax. The north part is the port for containers & guard by military. Pantai Ria Kenjeran in the east is not clean. The Mangrove park is probably nice.
I read this blog for food review :
http://www.inijie.com/