Picked up a cheap Subaru! Where to start?
 

I recently purchased a 93 Subaru Impreza L for $800. It is a 1.8l with 160,000 miles, front wheel drive and a five speed. I have put about 1000 miles on it and have seen an average fuel economy of around 32mpg, my worst mileage being 27mpg driving hard in the mountains and my best being 36mpg cruising on the highway.
My short term goal with the car is to average around 40mpg and I would love to hit 50mpg if possible. However I have no clue where to start!?

Check the head gasket. If it needs a timing belt, replace the head gasket, too.

Previous owner replaced the head gasket at 150,000 miles!

I thought all Subaru's were AWD?

Sounds like a great deal for under $1k wow! What are the plans for it?

I'd go with the basics just as with any vehicle. Start with good driving techniques, especially staying in the tallest reasonable gear for the given speed, and avoiding use of brakes by looking ahead and planning.

Consider a grill block if you can keep an eye on the engine coolant temperature. Put a little extra air in the tires. The basics.

Good fuel economy already!

Not the old ones. Subaru went ALL all-wheel-drive sometime in the 90s.

I don't know about the 1.8L, but the 2.0 or 2.2 with FWD around that era was specifically designed for efficiency...so you're probably starting off on the right foot.

Warm air intake, grill block, pump up the tires, check that everything under the hood is running right (spark plugs, plug wires, o2 sensors, thermostat, temp sensor), possibly upgrade to a heated o2 sensor, LRR tires when yours need replacing, alignment...adjust the nut behind the wheel...then it's time to start messing around with aero mods.

40 MPG are more likely to be achievable, but maybe some mid-40s on highway wouldn't be out of question without having to streamline the hell out of it.

After about 1996 Subaru became AWD, every model. Before that it was here and there, and earlier some of the models were 4WD rather than AWD.

I think you can hit 40 but doing much better than that will be a tall order. You have a better shot at it being FWD instead of AWD, reduced driveline losses helping you out there.

The usual: tire pressure (and alignment if it's new to you, no idea how long the PO let it go between alignments), brake drag, bearings if necessary, a few simple aero mods like a partial/full grille block, underside treatments.

Watch your temps carefully when experimenting with aero blocks.

You should be more or less okay with the head gaskets. Your car should have the earlier EJ22, which isn't as notorious for failures along those lines as the subsequent EJ25 or FA/FB engines. Pre-'96 EJ22s have a good reputation for being bulletproof.