Land at Midnight in Surnabhumi Airport

I would think a taxi is probably the best way but I've not done it.  Rate cards in taxis show standard rates to further places like Pataya and they didn't look so bad, but of course I don't remember them (at a guess, maybe still under 1000 baht).  Someone here might have more direct experience, or a forum like thaivisa is worth a look to ask, or to search for the same question, which has probably came up before there.

They have car and van services at the airport (they call limo, but using different types of cars or SUVs) and we've rented them after midnight for shuttling in town, and that should be an option, but more expensive.  A taxi might be a few hundred baht in town / Bangkok (not so much, $10 US) but those vans are over 1000, with the added benefit they can take more people and luggage.

Hotels tend to be inexpensive near the airport so an option would be to stay out there and travel the next morning.

Meter Taxi will get you there fine. Negotiate price up front before leaving with the driver though. Going rate is 1,200-1,500baht to Pattaya. Try and steer clear of the hawkers right as you get to the exit doors, ghastly prices.

The trip back to the airport should be cheaper between 1,000 and 1,200baht, the drivers know they are likely going to catch a fare back to Pattaya, so they are basically paying for the petrol to make their way back to the airport or BKK.

PS, Have a piece of paper with your hotel name and address handy with the telephone number so the driver can call and get exact directions to your hotel.

There it is then.  Note there is a taxi stand on the arrivals level that is the only standard place to catch a taxi.  You can get taxis elsewhere, like at the departures level, or the private cars (hawkers) mentioned, but probably as well to go through the standard process.

It seems like there wouldn't be much negotiating to it since they will assign you a taxi based on queue there, and there are rate cards in the taxis showing standard taxi-company rates, but in practice it might not be so simple.

In Thailand it's the law that taxis have to use the meters unless you request otherwise so there is a possible sticking point there; if they see it as their advantage they can claim they have to use the meter.  Those meters don't roll up quickly so 1200 to 1500 baht is a very long trip, likely about the same as quoted for the actual meter rate, but you wouldn't want the driver to try and search out the longest route to Pattaya.

Note that even in a central service provider location like a taxi stand, where you would expect them to be able to use English, they won't be able to, so any problems aren't going to be reviewed in English with you.  My wife has ended up translating in that taxi stand a number of times (she's Thai but speaks English), and even with the language issue sorted out that doesn't usually go well.  Given they are looking for any chance they can find to add a fee or surcharge it's better if she doesn't end up at that taxi stand at all. 

But you'll be fine.  A taxi to Pattaya is quite standard; how badly could it go.  I would read up on it in the thaivisa forum anyway, and possibly think through other related issues, like whether you want to try and get a SIM at the airport or not (maybe not an option at midnight).

I am almost willing to bet that you will not be the only foreigner getting in at that time, lots of late flights. If you happen to see some making their way to the taxis, just ask them if they are heading to Pattaya lol. Worst case scenario they say no, best case they say yes, you split the cab and toss the driver a split tip between the 2 of you of 100baht if heading to different hotels.

A lot of people arrange for cars or drivers they met previously on trips, so might be able to catch a ride with someone like that as well.

The minivans they have there will wait until they get nearly a full load before taking off, depending on the size of the van, 6-10 people most likely. I'm not sure on the price of this though, if I had to guess, would be somewhere around 500-600baht, but will drop you off at the front door of your hotel no extra charge. I don't know that it would be worth it to me for that route, especially if you end up being the last dropped off, the time you lose waiting to fill the van, plus the time to drop everyone off. Probably an hour or two on top of the trip itself, not something I would want to undertake after an extremely long flight.