Yes, but it is not only that. For city people who are accustomed to just walking to shops, restaurants etc. and are planning to move to Cyprus, I suggest getting an apartment in the very (touristic) center of the city. Even just a short distance outside of these places, the grocery/cafe/restaurant etc. options are very limited without a car (which creates its own inconvenience). The city planning differs from most of old European cities.
This is a car-centered society, but one needs a background︀ in other kind of society to understand that. There are a lot of people (esp.︁ Cypriots themselves) who just don't know what I am talking about.
In Larnaca a good place︂ would be Finikoudes and areas right behind it. Those give an easy, walkable access to︃ shops, restaurants and that great beach promenade you mentioned.
I don't know Nicosia that well, but as︅ mentioned, the old town around Ledras street is great (There, owning a car might be︆ a problem due to parking etc.). Nicosia is more city-like, so the walkable area is︇ relatively large.
(As to cars & driving, left-side driving is not difficult to learn, and︈ the lanes are often separated. Renting a car outside of tourist season is dirt cheap.︉ For example, right now an in-terminal rental, automatic gearbox, tiny Kia Picanto can be had︊ for 6,5 €/day.)