Hi travelman3
Just returned from a short trip in Shanghai and it is already very hot. Be prepared, that in July it is extremly hot and plan to do some sightseeing in the morning.
I lived in the north of Shanghai (Yangpu District), where accomodation is very cheap. But there it's a long way downtown and you better speak chinese, as there was not a tourist area.
I would suggest to book a room in a hostel:
http://www.hostels.com/cn.sh.html
Sometimes, there are also universites, where you can rent a room during the long summerholiday. But unfortunately I don't know which one.
Here are some things to do in Shanghai:
- Peoples Square with Shanghai Urban Planning and Exhibition Centre
- Temples: Longhua, Jing'an, Jade Buddha
- Yuyuan Bazaar and garden (very touristic but nice)
- Qipu Market (very cheap clothes, it can be very, very busy on weekends)
- Parks: Lu Xun Park (near Hongkou Stadium), Fuxing Park, Jingan Park
- The Bund (unfortunately last week we could not go there as everything is under construction)
- Jinmao Tower (you don't have to go to the bar and spend money, but enjoy the indoor view down to the reception)
- 1 hour foot massage (around 70 yuan)
You don't have to take the taxi to all these places. The bus system in Shanghai is very good, cheap (2-4 yuan) and most of them have air con. Just compare the chinese name of the place you want to visit from the bus stop and your map. A lot of shanghainese are very helpful and if you cary a small notebook with you, they write in chinese the name of the stop (which you can show the driver).
Check out the following link, maybe it will help you: http://msittig.wubi.org/bus/
Things to do around Shanghai:
- Hangzhou (Westlake)
- Suzhou (Gardens)
- Nanjing (about 3h by train, the purple mountain is really worth a visit and you can also find youth hostels in Nanjing)
Eating:
You don't have to buy your food in Supermarkets. If you go to all the small chinese restaurants in the street you can eat very good and cheap. In the evening you can find "Jaozi" (Chinese dumplings) or meetsticks from vendors all over the city. For both you only have to spend less than 10 yuan. You can also try the chinese restaurants and just point at one of the picture. Noodle soup costs around 10-15 yuan, plain rice around 2 yuan and some meetdish around 10 yuan.
Of course you can spend some days very cheap in Shanghai. But for this, you should at least speak some words in chinese. But as you know, there are a lot of chinese podcasts to learn it 
Sandra