The "bed" ain't for sleepin'. Starry nights at the old airport... Had a '71 Super Beetle Convertible - drop the top, push seats forward - undo seatback and plop that between front and rear - blanket on top & we were good to go-go-go.
I've owned an X1/9 too and will humbly suggest you check out a Fiat 124 Spider. The later cars have huge heavy bumpers, but those can be easily removed and replaced with smaller Abarth-style bumperettes for a few hundred dollars. Later cars have a 2.0L twincam that is pretty torquey for a Fiat -- upgrade the carb and exhaust and you're good to go. You really will be surprised at the power if you're coming from anything near a stock X1/9. Additionally, the parts are still quite cheap and the car has a good amount of 1960s Pininfarina style to it. I might be biased though....
I might be biased too: The only one I've ever ridden in must have had a leak somewhere 'cause it had rear wheel wells filled with cold water which sometimes came flying out over driver and passenger in hard cornering!
Guess I should not have sold my '95 SC300 w/2JZGTE swap, oh well it was a very nice and fun car. I'm jealous because that is one awesome car and a true sleeper. Now back to the topic have you considered a 1st Gen Miata??
How about an Alfa 164 sedan? Pretty available, and you should be able to get a decent one in your price range. Roomy, fun, more unique than a lot of the other suggestions, and pretty stealthy...
I would also recommend the 124 Spider I had one as my daily driver for over two years, if you take care of them they are very good little cars, plus they have 5 speeds, 4 wheel discs, and the parts are very cheap and easy to install, you can even install the convertible top yourself on these cars.
crown vic police interceptor. you can get them for cheap at auctions. mid 20's gas mileage. truck suspension and powertrain. i have a 98 i got for 4k. lotsa cheap parts if anything goes wrong. decent power and people are mighty polite when driving around you.
For a 944 to be rusty, it really really really needs to be abused and neglected. The bodies are galvanized, the ventilation flows through the rocker panels and other body cavities, and they have very thorough and high quality undercoating (and surface finishing) from the factory. Rusty 944s tend to be ones that have been in accidents or have been either driven in many winters and left to sit or in a saltwater flood and left to sit. Parts are indeed expensive compared to MGs and FIATs, but they are high quality and tend to last a long time. I think a 944 is a great balance of sportiness and practicality with the added bonus of good reliability, safety, and fuel economy. Another choice for $4000 would be an older (70s-80s) Mercedes SL. As with (probably more so than) a 944, a well-maintained example will be reliable to the point of boredom.
I was looking in this price range as well: saab, 944, alfa 164 or spider, and many mercedes were on my to see list but I l scored a taurus for free bought 300 bucks worth of parts and have been driving it for a few months now not fun to drive slow as hell and so so mpg but its comfortable safe and gets me around and was actually very clean inside and out and in good mechanical shape believe it or not. a 2001 in fact! Guy gave it to me after buying my car simply because he didn't want it! when it blows that list I posted will be the same one I consider for the taurus's replacement
Corvair Vintage Japanese.. think 73 Celica GT, B510 Ford Falcon - basically a Mustang without the looks Miata 91-96 Caprice, Caprice Wagon or Road Master Wagon (these things haul butt, and get good milage) Volvo V70 or 940 Early 90's convertible Celica MR2 Nissan 240Sx 5.0 Fox bodied Mustang
I ended up buying a 2000 VW Golf in very nice shape for exactly $4K. Very clean, drives nicely, so far I'm pleased with it. Needs a few very minor things but what 9 year old car doesn't?
Some say he drives a Golf, others say he has a Ball. All we know is... he's called the_stig. http://repairpal.com/volkswagen-golf-2000/recalls_and_tsbs