Well, in addition to the great case both rfmcdpei
have made for why Romulans should logically and by definition have numerous colonies, the novels have given us quite a few Romulan colony worlds:
Achernar Prime, Virinat, Xanitla, Ralatak (all now IRS, the latter three agricultural giants), Rator III, Terix II (a Romulan character in “Serpents Among the Ruins” is from here), Koruk (mentioned in “Vulcan’s Soul”), Nemor, Artalierh, Assaf Golav (a penal colony), Glintara (Another SAtR character was from here).
"Catalyst of Sorrows" stressed at several points the diversity of the Star Empire, and how some colony worlds were actually more advanced, technologically, socially, culturally, etc, than Romulus.
In addition, Romulans have always been shown as wanting expansion. Not resources. Not control. Not conquest for its own sake. Expansion. For many inhabitants of the Romulan Star Empire, their self-proclaimed “ideal” culture seems to be highly expansionist by default, and theoretically, when the economy isn’t in dire straits (which it has been since around the 2330s, apparently), Romulan national pride hinges in part on expanding the Empire. In TNG, it’s stated that at least some Romulans still believe they are destined to rule the galaxy. Evidently some branch of the government or some central tenet of the culture is promoting expansion. The fact that reality – in the form of economic concerns or powerful neighbours, or alternative ideologies within Romulan government or culture - is getting in the way of that ideal doesn’t change the fact that it’s there. There are definitely recurring expansionist movements within the Romulan government, we know that. Every few decades some coalition of frustrated nobles or officers are insisting the Romulans stop playing nice with the neighbours or hiding quietly behind the neutral zone and prepare to expand. There’s usually a strong dissenting voice, too, of course - but the expansionist movements keep cropping up. Expansion as an end in itself even seems to override hatred for aliens - the Romulan senators and officers in “Nemesis” were all for pushing past the borders and a new boost to the military might of the RSE, but had no desire to exterminate Earth. So it wasn’t a desire to lash out at aliens which was motivating them, but rather the usual recurring frustration at the lack of an expanding border.
If we consider the starchart on the Senate floor, as “Taking Wing” draws attention to - one of the Romulans’ biggest frustrations is always shown to be that in modern centuries they’re constrained by the neutral zone and other superpowers, chiefly the Federation. They clearly don’t appreciate having boundaries and barriers “imposed” on them, and every few decades there seems to arise a new crop of hotheaded leaders who want to try and test those boundaries, if the “static border” or occasional “pro-alliance” senate coalitions can’t stop them. Sure, there are long periods of relative calm and reason in between, when the Romulans typically turn inward and withdraw from galactic society - with the exception of some genuine diplomatic efforts between the 2270s and 2310s, before Vokar’s lot started up. But a significant number of Romulan leaders seem to place value on the pre-2160 days of rapid colonization and conquest. Even the very fact that they had a “Star Empire” to begin with means they looked out at those stars and desired to claim them - to reach out and establish themselves. So, in all, Romulans promote expansion. They colonize. It’s more than just a simple desire for resources (as with Cardassia); it’s an end in itself at times, at least for some Romulans. They don’t justify a conquest with “we’ll create some mines and ship this ore back to Homeworld” (though they might well do it). That’s
the Cardassians, because Central Command sets itself up as the saviours of the people, the benevolent but firm guiding hand that provides Cardassia with what it requires. The military in Cardassia provides the people with their basic needs. The Romulan military is always shown as embodying something more abstract – pride, honour, glory. The people who provide Romulans with basic needs are the farmers, etc. The military has a more lofty purpose, it seems- to be the proud Romulan Eagle showing its bloody wings. Romulans glorify in the noble pride and honour of the Empire. They're the higher society and they seek to seed the rest of space with their highness.