Is it okay to say, ‘He doesn’t want to go to anywhere’?

No, it isn’t. The word ‘anywhere’, like ‘somewhere’, is not preceded by prepositions like ‘in’, ‘at’, and ‘to’. We cannot say, ‘The Registrar is going to somewhere/anywhere.’ It is also important to remember that the words ‘there’, ‘here’, ‘upstairs’, and ‘downstairs’ are never preceded by ‘to’ either.

*The children are too tired to go anywhere.