（want to 以外で）「〜したい！」って英語でなんて言うの？

Other ways of saying 'want to' and 'would like to' include:
I intend to:
This means that you plan to do something.

I will
- This means you are going to do something

I desire to
- This means that you would like to or wish to do something.

I intend to clarify the previous statement by..
I will now discuss..
I desire to make it clear that...

I hope that helps!

▪I need to ...
▪I wish I can...
▪I require that...
●
Examples
a. I need to eat now because I am very hungry.
b. I wish I can go on a long vacation.
c. I require that product for my project.

With all of these forms, the context is important - and also, so is the amount of emphasis you may wish to apply to any statement.
"I want to go to the cinema this evening."
"I prefer a meal out, personally."
"I would like to go to Paris this summer."
"I have a great desire to visit Rome."
"I want to eat curry this evening."
"I dream of a traditional Japanes meal."

It depends a bit on what you are talking about for which you could use. For example it would sound quite normal to say "I have a strong desire to travel to Europe" but you would not commonly say something like "I desire a glass of water." Desire is probably a bit stronger in terms of your feelings.

I am hoping to is often used with any goals or future plans.

I wish to can be used quite casually. For example if someone is blocking a door you could say "I wish to get past."

example
"i don't really want to go".
or
"i do want to go".
or
"i intend to".
or
"i don't intend to".

I feel like.....- If you feel like you doing something it means that you desire doing it.
For example: I feel like going for swimming.
I wish to....-If you wish to do something it means that you are hoping to do it but due to a number of reasons you are unable to.
For example: I wish I can go to Paris this weekend.

Need is something that you really want, more than just a basic want.
Intend to is something that you will most likely definitely do.
Wish to is something that you want.