Frigidaire
Frigidaire is made by Electrolux. The sticker inside my dryer drum says "Augusta, Georgia"....I don't know if this is the plant location or corporate headquarters, but it does say "made in USA". However, my 1442 dryer is from 2006---to know manufacture information for current models, you'd need to check a unit in a showroom and look for the sticker.
I've had good luck with my 2140 washer, and most people post good experience with its sister model 2940. The Affinity series 6000-8000 was the one that seemed to have the problems. These are often sold at huge discounts, often below the price of the more basic 2140/2940 (which are still being made), as rp2813 warned above.
The "new" Affinity series, which seems to incorporate many features of the TOL Electrolux washers, seems much better, though only one or two posters here own them and can actually speak from first hand experience. They are:
4011: 4.0 cu ft, no heater but ATC
4272: 4.2 cu ft, with heater
4273-4274: 4.4 cu ft, with heater and steam
Retailers in my area offer the 4272 for the high 600s, and it's possible you could find a 4011 (if you don't need a heater) for about $600. The 4273-4274 are in the $750-850 range.
Due to the drop in home sales in the USA, fewer people are moving and that means fewer washer/dryers being sold. This seems to have exerted downward pressure on appliance prices. For example, the BOL Electrolux washer, which never seemed to go below $1200, is now approaching $1000 at some discounters.
If your budget is $600 max, you might consider a 2940. It was a Consumer Reports Best Buy for four or five years in a row. It has ATC but no heater. Also, in areas where water agency rebates are offered, the 2140/2940 often no longer qualify, having been overtaken by stricter EPA rules (for the era in which they were introduced, c.2004-5, they were water-thrifty). The new Affinity machines in general do qualify for water rebates, and gas company rebates in many instances. My 2140 qualified for a $100 water rebate and a $50 gas rebate, thus $150 back on a $600 purchase. My 2140 still washes great and is approaching five years of age. If I could do it over again, I would have chosen the 2140 for two reasons:
1. Auto Temp Control on the 2940, not on the 2140
2. Variable Delay Wash: fixed eight hours delay on 2140; variable delay 4-12 hours on 2940. I use this feature far more than I would have guessed when I bought it. It's great for setting up a load to wash and spin just before you wake up, return from errands, or come home from work. The 2140 eight hour feature is ok, but often I come home 12 hours after leaving for work and I don't want a wet load of clothes sitting in a sealed FL washer for four hours before I can remove them.