You actually have many options, and all of the suggestions above are good ones.
If you want to save a little cash, look at AMD. Just be sure to get the newer Vishera cores. (4300, 6300, 8320, 8350) If you don't want to overclock, the 6350 is a good option since it has higher base clocks and will perform well without any overclocking. Couple these with a motherboard that has at least a 970 chipset, and go for a 990FX chipset if you can afford it. ASRock and Gigabyte have some very good options that are also affordable.
Avoid the older Bulldozer cores. They won't perform as well. (4100, 6100, 8120, 8150)
If you do not plan on OC'ing and you want a CPU who's performance is close to the i5-3570k, then you are basically excluding all AMD CPUs.
The obvious CPU to choose is the i5-3570. It is the locked version of the i5-3570k. The other option would be the i5-4670. There is also the i5-4670s which consumes less power than the standard i5-4670; 65w TDP vs. 84w TDP. The base clockspeed is 3.1GHz instead of 3.4GHz, but both CPUs can reach up to 3.8GHz with Turbo Boost.
There is also the i5-4570 series. The max Turbo Boost speed on these CPU is 3.6GHz. There i5-4570 has a base speed of 3.2GHz and a 84w TDP. The i5-4570s has a base clockspeed of 2.9GHz and a 65w TDP. The i5-4570T also has a base clockspeed of 2.9GHz, but with a 35w TDP. However to achieve this low TDP the i5-4570T is only a dual core CPU with Hyper Threading.