The more places the better, but planning is important.
Most people new to puppy training would tell you that their puppy understands the basic commands pretty well at home. Yet, they are often very frustrated when their pup has no idea what is being asked of it when they take it out into the world. This is very common and can be easily corrected if you take a little time and plan your training sessions.
Your training plan must including different environments and settings. This may seem a little odd as dogs are not the best at generalizing behaviours. For example, Fido will sit and come when asked at home but speaks a different language when you’re at the park, or going for a casual evening walk.
I suggest that you try to find a few different places to practice your basic training. The key is this, if Fido does not listen in new environment, then go back to the basics and practice those same behaviours in that new environment and take it slow. Don’t forget to use high value treats to keep Fido’s focus on you. If there are distractions that are too strong, get better treats or move a little farther away from them.
Just remember, have realistic expectations for your new pup.