It was my first time in this city. It was my first trip/visit to this city. It was the first time I visited this city. It was my first visit/trip/time here.

It was my first time in Australia. It is my first time in Australia. It was my first time visiting Australia. It is my first time visiting Australia. However I would try to avoid using these: It was my first time to visit Australia. It is my first time to visit Australia. They are all correct.

I would add that, if you are talking about a past occasion (which I assume from use of 'was'), then 'the' or 'that' might sound more natural than 'this'.

If you say 'this', it sounds like you are still in the city, and therefore wouldn't be using a past-tense form, unless you were perhaps looking at an image of it.

It was the first time I had visited that city (I'm not there any more)

It was the first time I had visited the city (I'm not there now and to use 'the', I have probably already told you the name of the city in a previous sentence)

It's the first time I have visited this city (I'm still in this city)

:-)

It's the first time I have visited this city!! This is the great form, friend!!👆👆