Does your character not seek medical attention?
Does your character seek help, but die from allergic reaction to the antivenom?
Are you looking for a native species?
http://www.esf.edu/pubprog/brochure/snakes/snakes.htm
Rattlesnakes don't climb trees or stucco walls, but they could make their way onto a play ground designed to allow small children access.
We've had rattlesnakes climb up into the wheel wells on the pickup, and get up by the engine.
How old is the character? How soon is it between the bite and death?
I'm a bit skeptical about the "death by snake" plot point. Is it intentional, done by someone trying to make it look like an accident?
There are very few snakes in the world that can kill you dead before you have a decent chance to reach a hospital (assuming you're not in rural isolation hours away from help).
Snake antivenom is very specific to species. Even with rattlesnakes, the most effective antivenom for the bite is going to be for that specific species so proper ID is very important. If the character doesn't know what bit him or misidentifies it, he might not get the correct treatment and that could easily lead to his death.
It's also very expensive, and difficult to store. If a venomous snake is not native to the area the hospital definitely will not have the antivenom in stock. Several years ago a zookeeper was bit by a gaboon viper from her personal collection. The animals at the zoo were venomoid, but for some reason she didn't have the surgery done on her own animals and no hospitals in the US stock gaboon viper antivenom. She died. They found her clutching a note that said "Call ICU", that's how fast the venom can work.
So native snakes:
Massasauga: They're endangered and only found in two places in the state. Also very very shy.
Copperhead: Unless the victim is a very very small child and people don't notice that it was bitten until too much time passes, I'd have a hard time buying death by copperhead. They'll generally make you really sick, and the antivenom is readily available all over the east. People rarely die from copperhead bites.
Timber rattlesnake: Also very shy and have a limited range. The problem with having any rattlesnake in the middle of a city, is it won't be there naturally. They are very afraid of people. They den together with close family members, and don't usually leave their home range by choice.
If it's really necessary for your character to die by snakebite, a nonnative is most plausible.
If you want it to be obvious that your character was killed by a snake, you either need to have the snake be present (like it bit the character and he killed it so there's a body that can be ID'd) or it needs to be an obvious snake bite wound.
Vipers (rattlesnakes, copperhead, etc.) are hemotoxic. Their venom causes tissue death. Google "rattlesnake bite" if you have a strong stomach, because it's really gross and very distinct. If he's bitten by a non native viper and they try to treat him using native viper antivenom it won't work very well.
Elapids (cobras, coral snakes, brown snakes, etc.) are neurotoxic. They cause death a lot faster, but the cause is a lot more subtle if people aren't looking for snakebite. It's more along the lines of heart problems, difficulty breathing, paralysis, etc. I'd avoid them unless you have someone kill the snake at the time of the bite.
If police decided it was an accidental death, they'd probably depend on animal control to find and trap the animal if it was still at large. Sometimes animal control contracts with local herpetologists experienced with venomous snakes for safely trapping and removing them.
I met a guy who was the venomous snake removal guy for a portion of Virginia. He forearm was pretty messed up from the time some 19 year old guy living in his mom's basement decided it would be cool to have tons of eastern diamondbacks as pets. The shelves with the tanks collapsed one day and he got called in by AC to trap the half dozen rattlesnakes loose in the basement.
He got nailed on the forearm by a very freaked out 8 foot diamondback. It dumped such a huge load of venom in him he would have died except that the fire department was literally five feet behind him and able to start first aid immediately. A large portion of muscle in his forearm died and never grew back.
Many snake bite deaths are related to alcohol use as well. Snakes aren't very confrontational. People drinking alcohol do very dumb things sometimes. It also impairs judgement when they're deciding what to do about the bite, and with a bite every second counts.