These are my interpretations:

For the most part, people will just go to see the sights and have a good time. -- Describes what people will do in the future, or, with less of a direct sense of the actual future, describes people's general habits (what they are generally expected to do).

For the most part, people are just going to see the sights and have a good time. -- This could mean either of two things. It could mean that people are (now) travelling somewhere purely in order to see the sights and have a good time. Alternatively, it could mean that when people (generally, in an abstract sense) are in the place referred to, the only thing they are likely to want to do, or have the opportunity to do, is see the sights and have a good time.

Both men & and women will have many new adventures. -- Ordinary future tense; nothing much further to be said.

Both men & and women are going to have many new adventures. -- No discernible difference in meaning to me.* (However, it is possible, though to me unlikely, that "going" here could again mean "travelling somewhere".)

*Edit: However, the "going to" form is more conversational.