1. it's a euphemism for whorehouse/brothel
2. she should go become a nun because all men are depraved beasts, him being no exception
3. If she goes to a convent, you can make the claim his intention is if I can’t have you, no one will. If he’s talking about a brothel, that’s just hateful.
4. Per u/jakopappi -Hamlet at this point in the play is beginning to realize that he just cannot let the idea go that his uncle has killed his father, then starts banging his mum, and steals his kingdom. Hamlet up to now has been expected to marry Ophelia, and indeed is fond of her. But he finds out her father is complicit in the effort of his mother and uncle to "handle" him by sending him away. A trip from which he will never return. So he tries to spare her by pulling the it's not you it's me line here. But she knows better, and feels the gravity of all of the goings on in this medieval castle because she's smart enough to see what her eyes have seen and ears have heard. She wants to support him, to help him, the only way she knows how, by loving him. And he tells her she should give her body and soul to christ (nuns at the time were "married" to christ). Essentially, she is worthless to him. And to any man. And she's crushed.
5. Per u/Wrought-Irony - nah man, he's telling her to give up on him because of how big of a shit he is and how all men are shitty and she'd be better off at a nunnery. He thinks he's being kind by telling her he never loved her, and she should avoid him and all men, which is why he starts by saying "I did love you" then pulls it back a bit "once" then pulls it back even more when he says "you should not have believed me [when he told her he loved her]" the nunnery bit is also kinda like he's saying he doesn't want her, but at the same time he doesn't want her to be with anyone else because he actually does care for her, so he suggests she become a nun.
6. Per u/xo3k - Alternatively girls who got pregnant out of wedlock might also dissappear to a nunnery for a few months, before returning alone. This interpretation of his instruction makes a number of the following lines sound like reasons to give up their child, perhaps even to abort it. I've always preferred that interpretation because the added cruelty of him giving up not only on himself and her, but also their child, does a far better job explaining her rapid decent into madness and suicide.
7. Per u/BackupPhoneBoi - Hamlet is very emotionally unstable at this point in the play. He just had his "to be or not to be" soliloquy right before this interaction. Ophelia denying his love only adds to this emotional instability and Hamlet acts out against her and humanity in general. He tells her that he really doesn't love her and the lines right after this video is him saying if he had to give her a wedding present, it would be an STD. The double entendre of the nunnery adds to the malice Hamlet displays in this scene. Hamlet is either completely losing it or dramatically acting for Claudius and Polonius hiding in the background. The layered meaning of phrases like "get thee to a nunnery" only adds to the theme of uncertainty that is poignant throughout the play.
   Hamlet absolutely would use crass misnomers of religious institutions and Shakespeare would absolutely have double entendres, especially in pivotal and emotional moments, that give more emotional depth to these scenes.
8. Per u/Momoneko - I'd say not only men, but his point was that existence as a whole is an ugly thing and she should not make any more human beings if she can help it.

Why wouldst thou be a breeder of sinners? I am myself indifferent honest but yet I could accuse me of such things that it were better my mother had not borne me.

What should such fellows as I do crawling between earth and heaven*?