Tom,
You can find an acceptable (clean, functional, furnished), 1-2 bedroom apartment in Suzhou for 2,500-3,000 RMB's (~$400-$500) per month, which should include utilities (gas, electric, water, cable TV, high-speed Internet). It won't be in the center of the expat community, nor in the hovels down some ancient alleyway. You'll be within walking distance of a big box food store and shopping malls. But if you want to spend 4 times that amount for rent only, then you have that option too.
Suzhou has one of the most expensive standards of living in China. Western-style bars and restaurants charge about the same you'd pay in the States. You'll save a lot if you can stick to living just outside the expat boundaries and by their standards. It isn't that tough to do. You'll also learn more about Chinese people and culture if you live closer to the older part of the city, emersed with the locals, instead of being isolated in the Western-like new subdivisions.
Food items from the West are packaged goods (cans, jars, boxes, bottles, frozen, preserved meats, etc.), and they will cost 2 to 4 times the price you can buy them for in the States or Europe. Local food (unpackaged, uncooked) will be cheaper, but don't expect the same quality or health factors as you might expect in the States. There is plenty of cheap and healthy Chinese food, but it isn't always easy getting both at the same time. You can eat all your meals in an endless number of restaurants serving Chinese food for 100 RMB's (~$16) per person per day, or for much less depending on your preferences. A previous contributor's earmarks were on the money: 20 to 200 RMB's (~$3 to $30) for food per day.
About clothing. If you're stopping in the States before arriving in China, you may want to stock up on essential clothing items that suit your tastes. It isn't easy for all Westerners to finding clothing in the same size, quality, and selection as you'd expect in the States or Europe. Count on spending 50%-100% more for Western-grade clothing. Those items are often considered luxury items, which are subject to import taxes and premium charges by the sellers.
Transportation is another expense issue. You can buy a good bicycle for getting around town (plus get a cardio workout) for $200-$300. A one-time expense--unless it gets stolen. Tip: buy at least two chain locks. If your bike gets stolen (likely) you can think of it as renting the bike for an unspecified period. Still usually a good deal. Really cheap Chinese bikes cost about $35 (not recommended). You can buy a new e-bike for ~$250, or an electric scooter for ~$400. Depends on your hunting and bargaining skills. A taxi ride will cost about $1.50 (10 RMB's) for the first 10 minutes or so of in-city driving. A 20-minute ride may cost you 30 RMB's (~$5). A private driver will cost about 500+ RMB's (~$80) per full day. Walking and buses are the cheapest options, but there are drawbacks with them. Owning or renting a private car for you to drive yourself is a whole different story.
Traveling to further destinations . . . . Taking the high-speed G-trains (300+ kms/hr) from Suzhou to Shanghai (23 minutes) will cost 40 RMB's (~$6.50, economy class), and 100 RMB's (~$16, economy) from Suzhou to Nanjing. Economy class is more than comfy enough for those shorter rides. Business class will add about 50% more. You can take a high-speed train to Beijing for $100 +/-, and be there in a half-day. Much better than flying, because you see more out the window and it takes about the same overall travel time door-to-door. And you don't have to strip to your underwear to get on a train. Taxis in those cities are a little more expensive than Suzhou, but still a good deal. The subways in Shanghai, Beijing, and Nanjing all offer the cheapest in-city options if you don't mind walking a bit. At the lower end, you can stay in acceptable (sigh) 3-star hotels for ~160-320 RMB's (~$25-50). Best to see the room in-person before you pay. Prices go up from there. Airfares are in line with Western pricing for similar distances.
Tourist attractions--gardens, museums, parks, etc.--range from free to 100 RMB's per visit. If there is a charge, it typically costs 40 to 80 RMB's ($6.50-$13). There's a wide-range of modern day entertainment options (movies, concerts, etc). Of course your discretionary expenses are up to you. There's a lot to be experienced in China for free.
You can get by more than well enough on $2,000 per month or less if you're willing to make a few adjustments here and there.