What would be the/a correct way to say "I have something to myself"? For example, I wanted to say "I have the house to myself this weekend". I said "Tengo la casa a mi mismo". That felt wrong, but I couldn't find another way to say it.
You only use "mí mismo", "sí mismo" and the like when the person is the main subject of the sentence, e.g: "Se hace daño a sí mismo haciendo eso" (he hurt himself doing that). For language economy we tend to omit it and only use it to add emphasis, because the rest of the sentence has to conform with the subject and so the target is already implied (although it is not redundant to add it, it's correct).
If you say "Tengo la casa para mí mismo" it will sound like "I have the house for me myself", and is actually not a correct use as the main object in question is "house".
You can simply say...
and it will already imply that its just for you. You can also say...
and you will emphasize that you are alone, but it can also imply that you want it to remain that way, or are forbidden to bring anyone else in. Beware that if you say...
means that you have the house only this weekend.
An easy way to find out if you should use "* mismo" is to ask "who?". If the anwser is not he/she/it, then you should not use it.
Fun fact: Spaniards have problems with the use of to and for, and in english I would probably end up saying that I have the house all for myself :P
I would say: "Tengo la casa para mí este fin de semana". If I'd like to emphasize the fact that it is to myself and nobody else: "Tengo la casa para mí solo este fin de semana".
That probably sounds a bit familiar. If you want to be more formal you could say "Dispongo de la casa [para] este fin de semana".
... if I understood the original intent right (would it be roughly the same as "I have the house for me"?)
To emphasize that your are the only one to enjoy (or work on) the thing, you could say
I wouldn't say "Tengo la casa para mí mismo", it sounds wrong; that would be right only when there the subject (or the agent) of the phrase is also the object. Eg: "Me golpeé a mí mismo" (I hit myself) "El regalo lo compré para mí mismo" (I bought the present to myself)