The Chinese have the prices set for everybody for the major attractions so you do not get special tourist prices, and a lot of the prices are written down for you to see in places that you might not expect like hotels. The temples and the tourist spots have many Chinese there visiting them, and they are as interested in you as they are the cultural attraction.
Any of the markets will offered many things to sniff taste and play with. I bought some magnets that were providing hours of fun for a couple of dollars, only to have them taken away when I went to get on the plane to come home, a major bummer for me. I also bought a coffee cup that changes scenes when you put hot liquids into it.
Everything emanates from the center of town which in Beijing is The Forbidden City. Surprisingly taxis were expensive, and the buses a little hard to understand, but the metro is a breeze to use and cheap at only 3 Yuan a trip. Using only the metro does limit you a bit when you go out to the outer rings, but in the city center it will get you everywhere.
The first thing that we tried to do was go to the Great Wall at Badaling using the Beijing city buses only to find out after a day of looking that the buses were incorporated into a tourist service, and the buses we were looking for were no longer named what was on the tourist map. We spent the better part of the day looking for them, but we still had a great time as it took us places that we probably would have missed, in particular a side street that paralleled the Forbidden City that was a neighborhood of hutongs.
Inside the 2nd ring is a treasure trove of interesting things between the Forbidden City and the railway station on the south end was an old part of Beijing's city wall, a shopping maze with small stalls and little fast food noodle shops. The area around the train station had old luxury 5 star Chinese hotels, Beijing cheap guesthouses, massage centers and restaurants that for the curious offered allot of amusement in their design and function. You could spend a couple of days in this one small area and still want to go back to find more.
If there is a secret to seeing the real Beijing on the cheap it would be get lost for a few hours heading in random directions.