You’ll want access to an indoor pool for most of your training. This will allow training regardless of the weather. Ideally, you’ll be able to join a gym or university athletic club with a half-Olympic or larger pool. Make sure there will be blocks of hours set aside each day for lap swimming.
If you plan to compete in triathlons with open-water or lake swimming, you’ll absolutely want to complete some of your training under similar conditions. This means a suitable beach with a lifeguard presence, or a lake with other triathletes who watch out for each other—never swim alone. You’ll find that the wind and waves present challenges unlike anything at the pool. If you can arrange for group training sessions at the beach, you’ll be able to practice for the added challenges of a mass-start race, including turbulence and general chaos.
Nothing beats the open road, if you can find a route with reasonably safe traffic and a good shoulder. If you’re not sure, consult with local bike shops and cycling clubs. Google Maps now offers guidance and routes that are safer for cycling.
Bike paths are also a possibility, but you’ll want to avoid peak times, like weekend afternoons in the Spring and Summer. It’s both difficult and unsafe to train on a crowded path.
In the winter when roads become impassable, you’ll be well served by an indoor trainer. There are many that simply mount to your regular training bike, providing resistance either through fans or magnetic inductance. Some are quite sophisticated, with sensors that sync to computer monitors for a virtual cycling experience. These use software to logs your training statistics and can vary your virtual course to match your training program. But even the most basic trainers do the job just fine. Be sure to use a towel to protect your bike and the trainer itself from dripping sweat.
You’ll probably find many choices wherever you are, including roads and paths in parks. Don’t hesitate to contact local running clubs or running shoe stores for tips.
The primary considerations are convenience and safety. Consider the dangers of both traffic and remote unpopulated parks and roads.
If you live somewhere with long winters, you may have to do a significant amount of training on gym treadmills. This requires a bit more mental stamina than running outdoors (and possibly some good playlists, podcasts, or recorded books)—but it’s fundamentally similar.
A great benefit of triathlon is that it doesn't require specialized facilities. You can accomplish a significant amount of your training on public roads, paths, and beaches. You’ll want access to a pool, but in all but the most remote locales, you should be able to find one.
Do take advantage of local swimming, cycling, and running communities when looking for tips. Stay safe, and enjoy the training process.