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Regarding hotels, let someone else comment, but expect that prices for 'nice hotels' are at the same level as in Tokyo and Manhattan.

Walking tours do exist, but to me they do not worth the price ($150 and more for 3h) they charge. You can walk in all these places on your own and see everything.

For art - Asian Civilization Museum and National Gallery is a good start. For architecture and history - walk around Telok Ayer/Chinatown/, Joo Chiat and Geylang areas with traditional shophouses. Modern architecture you have at Marina Bay, Gardens By the Bay (must visit both cooled conservatories), Pinnacles @ Duxton (go to the top on Level 50, entrance is at the ground level at Block G, costs $6 to go to the top), Star Vista and other places.

Visiting Singapore City Gallery is must to understand how city is laid out, what are current and future planning. Note that it closes at 4PM on Saturday and is closed on Sunday.

Food - avoid touristy places, particularly Marina Bay Sands, Lau Pa Sat and Newton Food Court, plus probably Orchard Road as well. You can go pretty much any other food court, especially in non-touristy areas and you will get really good deal, if see a line next to a stall, usually it is a sign that food there is great. Recommended food courts are at Tiong Bahru, Zion Road hawker center, Old Airport Road Hawker center, Geylang street eating places, closer to the city center - Amoy Street hawker center and Maxwell hawker food center. There are plenty of choices from dozens of cosines (but mostly Asian, don't expect to have nice Italian dinner there), so non-seafood options are plenty.

Massage - average prices start from SGD $60 for 1h outside of city center areas and sky is the limit, some places at Orchard charge $260 for 30 min, massages at nice hotels expect to be in that range. No, never been. Locals go for massage (and shopping) to Batam and Johor.

For non touristy areas you need to get out from downtown core and go where local live. Number of suggestions - Punggol with walking to Serangoon Island, Changi Village and Pulau Ubin, and hearlands, like Khatib, Jurong East, Ang Mong Kio, Bedok. Close to the center but still local/non touristy - Tiong Bahru.

If you like nature, walking at Singapore Botanical Gardens, Sungei Buloh Wetlands park is must. East Coast park is almost 8m stretch flat walking overlooking the bay. You can download Ofo and Mobile app on your phone and get one of these shared bikes to see the area, charges are $2 per one hour.

Shopping - you will have to look really hard to find anything 'indigenous to the culture' - Singapore imports everything, including water. Anything you find in shopping malls/centers are either extremely expensive (Orchard rd, Marina Bay Sands and similar places) or cheap stuff made in China. One exception might be Peranakan Tiles Gallery at Teloy Ayer street which sells antique tiles, definitely worth to visit even if you don't buy anything - you will see number of different tiles used to decorate shophouses in the area.

You won't have language problem, English in primary language pretty much for everyone here. As far as sweating - well, if you have been in Houston/Florida in August, it is pretty much what it looks like.

I'm sure others will step in and fill gaps.

P.S. For evenings - at Esplanade theaters every evening from 7 till 10 they have free concerts. garden Rhapsody at Gardens By The Bay are played twice per evening, plus there is a light show at Marina Bay in front of Shoppers/Marina Bay Sands.