Auburn is closer to the American River - where we have enjoyed swimming.
This is easier to get to - its by the bridge on highway 49 - south of Auburn and you will see many parking along the road, etc. You then need to walk down to the river - but its pretty easy to do and enjoy.
While both towns are small town urban center than they used to be (we have relatives in the area), both Placerville and Auburn have some unique charm about them. If you are looking for gold rush towns, Sutter Mill is closer to Placerville.
so driving to that area will give you the most historic feel.
We recently stayed at the Best Western in Placerville (it was close to where we were having a family party). It is a nice place to stay. You have to pay a bit more, but they have pool side rooms. (you have access to the pool regardless of where you stay in the hotel but it was great just stepping out of our room into the pool area). So if you want just a place to swim and be in the jacuzzi versus a swimming hole, it might work for you. If you want a natural swimming hole, the American River is better to swim at. At the BW, there is a Mexican Restaurant within walking distance that is good to eat at.
We have not stayed in Auburn but they have various lodging to stay at. Look at the hotel section of trip advisor - or perhaps another person can advise better than I can.
Edited: 11:46 pm, June 17, 2012