Fuel-efficient, low-maintenance, affordable

Gen 3 Toyota Prius is the answer you're looking for. With these don't be afraid of a car with over 100k miles (althought I'd personally avoid one with mileage > 200k). I brought a 2010 with 140k 1 year ago for under $6500.

If you have access to a parking space / garage with a plug and your daily drive is less than 50 miles (between charges) consider a Chevy Volt - it's more fun than the Prius and has provent to be very reliable. Biggest downside it lack of rear legroom vs a Prius.

Pre 2012 focus aren't bad but htey stoped the hatch version back in ~2006. For newer than 2012 only look at Ford Focus with a manual - the dual clutch transmissions are plagued with issues.

I have a 2005 Prius with 250k miles and a 2016 Prius. They have been some of the best cars I've owned and I've never owned a car that long. I've only replaced the battery in the 2005 a few months ago. No other problems other than a few recalls and a rattle in the C pillar of my 2016 fixed under warranty. Such amazing cars.

I agree with colin42, get one with less than 200k miles, preferably an already replaced hybrid battery and 2010 was a major redesign. colin42 got an amazing deal, so don't expect that low price, maybe around $10k. That's probably the only thing that will go wrong with the car aside from burning oil, $2000-2500 fix once every 150k-250k miles.

The Chevy Volt really hasn't had consistent reliability as only the 2015 and 2013 had good ratings on Consumer Reports. Then there are the problems of being a 4 seater and it needs premium fuel. It would be my choice for a PHEV except for the Prius Prime. The Prius has had 5/5 perfect reliability scores every year except for 2001 and 2006 where it got 4/5. Also, the Prius has had excellent consumer satisfaction scores across the board, which is rare for their used car satisfaction rating system (I've never seen that high satisfaction on CR). This is true information, but I may be biased since I own two of them.

The Mazda3 is a great car; 2014 was a major redesign. It isn't the most comfortable compact car, but it is fun to drive. To make it lighter they take out sound deadening and as a result there is a lot of road noise. I'm not a fan of the Malibu or especially the Focus. Boring cheap tinny rental cars. The upside is a huge depreciation hit. Only the 2007-2011 Focuses or Foci were reliable-ish. That generation Malibu was mostly reliable except for a decent amount of transmission failures.

For the Volts as I said if you go < 50 miles between charges it's operating cost would be lower than a Prius even with preimum fuel (This assumes 35 mile electric range and ~ 10c / kW.h)

https://www.truedelta.com/Chevrolet-Volt/repair-frequencies-1048

I'd look for a 2013 or newer as they included the hold feature that allows you to force it to use the engine mode when the battery isn't depleated. However now checking KBB this may be above you budget.

The Prius prime came out in 2013 but with only 11 miles range.

As for 2010 prius prices for an average milage (~90K) and dealer price you might be looking at the top of your budget but with ~140K miles and private party you right at the $6500 mark. (https://www.kbb.com/toyota/prius/2010/iii-hatchback-4d/?category=&intent=buy-used&pricetype=private-party&condition=very-good&persistedcondition=very-good&options=&path=&vehicleid=371241&mileage=140000)

The Prius Prime came out this year as a 2017 model. In the past they had the Prius Plug-In from 2012 to 2015. It was a good car but there was no reason to get one over a Volt with the useless EV range. It was just a Prius with a longer EV range and was pointless. As a used car it will be a better deal though.

I did the KBB 5 year cost to own comparing and the Prius is a grand cheaper, which is a negligible difference for most people.

Like most EVs/PHEVs the Volt has a huge depreciation loss. Higher mileage ones near me in SoCal are $8k-12k. Ones with less than 100k miles are $14k and up. PHEVs like the Prius plug in, Prime, and the Volt also are eligible for carpool lane stickers, something I had with my Prius and really miss since they expired.