keyword strategy for multiple cities - Keyword advice???

I have some questions about keywords and what tactics to use on the website?

I have a company with headquarters in one city where most of the work is done. Reception offices in two other cities.

As I have now, my front page is H:1 "lawyer my name" and I am no 2-4 on google in my hometown. However, the keywords from my landing pages are cannibalized across each city and the other way around. There I have H:1 "Lawyer city" on each city. In the other citys I rank no 1-2 and no 8-10.

Should I use the keyword "lawyer city" on the home page and remove the landing page where I have a page for the main city and only keep the other cities?

Most of all the links are my company name Lawyer xxx and head office address.

Do you have any tips on strategy?

Its bit difficult to understand (what city/ country/ cities) without looking into your website but as per your standard query - I suggest you to follow Silo Structure for SEO.

Steve