I agree with AcuraT that the 2014 and newer Mazda3 is a great choice. We bought a 2015 i Touring Sedan for my son in December for $14,500 (20k miles) and it is truly a fun car. It isn't quite as nimble as my old Miata, but it comes very close. By the way, the Mazda3 Sedan has been available since 2004. It isn't as desirable, but it was a few grand cheaper with the same amount of features and is still beautiful. One benefit is the Sedan is 100 lbs lighter than the Hatch. It has the best quality interior in a car cheaper than $30k, beating out the "luxurious" Buick Encore (the Mazda3 won an award from Road & Track for that). The ride could be softer, but you have to trade some comfy ride for handling. Road noise is also louder than its competitors. Overall, if you want reliability, fun handling, styling, and a nice interior with tons of features, this is the perfect package. Cargo space in the Sedan is significantly smaller than the Hatch. It will give you almost-GTI handling, but without the headaches. You might miss the German feel, too. Mazda's CPO program comes with a 7 year/100k mile powertrain warranty and a 1 year/12k mile bumper to bumper warranty. These Mazda3s are right in your budget.
All of danlisahall's suggestions were good, though I've never been a fan of the Forte. I don't think you'd like the Forte coming out of a Golf. I've heard that the previous gen Fit is fun to drive and the latest one isn't. The amount of stuff you can fit in a Fit is astonishing and it is super easy to maneuver.
Norm, the figure-8 course measures grip, not really handling or steering feel. The results could be because of tires or safety aids. What the driver actually feels is what matters.
As C&D put it, "In any case, it's clear that getting pinned against the seatback isn't part of the appeal with these vehicles. But on other portions of the dynamic scorecard the all-wheel-drive Encore acquits itself pretty well. Brisk maneuvers bring an abundance of rock 'n' roll, but the steering is reasonably quick (2.8 turns lock-to-lock) and more tactile than some. And the payoff for suspension tuning that favors compliance over roll stiffness is ride quality that's benign even on washboard unpaved roads.
We weren't able to document grip for this Encore due to snowy weather conditions, but expect it to be similar to the so-so 0.81 g recorded by the front-drive model. On the other hand, its 166-foot stopping distance from 70 mph is among the best in the class."
Consumer Reports said "The Encore's small footprint makes it highly maneuverable and easy to park in tight spots, but agility in everyday driving falls short. No one will confuse the Encore with a Mini Countryman or a Nissan Juke. Handling is sound but unexceptional and the tall and narrow stance take away from a sporty feel. Turn-in response is reasonably prompt and body lean is fairly well contained. The steering is well weighted and conveys a hint of feedback."
Motor Trend said, "The Buick's cushy ride is great under normal circumstances, but the subcompact does not like to be pushed too hard, thanks to the high amount of body roll, making the Encore not very fun to drive. However, the crossover still fared well in our figure-eight handling test. It took the Encore 27.8 seconds to lap the Motor Trend's figure eight, slower than the 2015 Mercedes-Benz GLA250 4Matic's time of 27.0 seconds but faster than the 2016 Honda HR-V AWD's 28.0 seconds. The 2013 Encore with the standard 138-hp engine took 28.2 seconds to lap the figure eight.
The Mercedes-Benz GLA250 and Audi Q3 have starting prices in the low $30,000's because those are true premium crossovers with plenty of luxury and performance. The Encore just isn't. The nonpremium powertrain, aggressive start/stop that rattles the crossover, lack of fun handling dynamics, lack of standard leather upholstery and a front passenger armrest, and tiny rear seats that significantly diminish front seat room when folded down makes it a premium hard sell."
I thought you were a driving instructor. A car can put up good grip numbers, but that doesn't say anything for handling as these three reviews prove. They liked that it was maneuverable in a parking lot, but handling at driving speeds was bland and squishy. There is a reason Buicks don't compete with the GTI or Mazda3;they are tuned for comfort, not handling. Nothing is wrong with that as long as you don't compare them to cars that are meant for handling. You actually can't get much farther apart from a GTI and an Encore in terms of handling when comparing the same size car. Try to recommend cars with some thought, Norm.