The lLast week, I visited my old house.

You could also say "This past week". Still natural-sounding, but less common.

Usually I love to approachvisit to my old neighborhood, because I remember my friends.

Not a grammar note, but I would recommend removing "usually" unless you no longer love it. I understand that you stopped visiting, but the "usually" here is tied to the verb "love", not "approach".

I replaced approach with visit because I think it's the more applicable word.

iIn this neighborhood, I lived numerouswent on plenty of adventures, but unfortunately I had to move to a bigger city for work.

The lLast week, I visited my old house.

Usually, I love to approach tovisit my old neighborhood, because I can remember my friends.

in this neighborhood I lived numerous adventures,I had numerous adventures in this neighborhood, but unfortunately, I had to move to a bigger city for work.

The lLast week, I visited my old house.

Usually, I love to approach tovisit my old neighborhood, because I remember my friends.

in this neighborhood, I livexperienced numerous adventures, but I unfortunately I had to move to a bigger city for work.

If you want to just say 'unfortunately I had to move to a bigger city for work', you would need to put it into another sentence like this: 'Unfortunately, I had to move to a bigger city for work'. Or you can do it as I put it in my correction, using the conjunction 'but'.