I'm fascinated by the idea of small city-states being able to punch far above their weight class, but mostly overseas. They had a far harder time dominating their own "countries." Athens couldn't conquer the mainland Greek states, and Venice, Genoa, Pisa, etc, did poorly when they tried to dominate the other Italian city-states.
Part of the picture is clear — they had plenty of money from trade, which gave them resources they could use to conquer overseas territories.
But Look at Pisa, as an example. Pisa's fleet and army made conquests on Sicily Northern Africa, Sardinia, and the Balearic Islands, feats of logistics and manpower that even major powers like the Byzantines and Romans had failed at. Many of these places had strongly placed defenders and considerable resources. Why were the Pisans able to defeat them with relative ease, but they could make no inroads in Italy proper?
More broadly, why did this model work to an extent, but never really allowed the city-states to become larger empires?
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I could add Carthage to the list, but they seemed to hold a lot of territory in Africa, which perhaps makes them more of an empire with lots of overseas holdings and strong fleet/merchant marine rather than a "maritime city-state with imperial ambitions."
I can only really speak for Venice here, but it would likely be the same for its Italian rivals - Pisa, Amalfi and Genoa.
Simply put, they didn't want land that wasn't of strategic maritime interest. The Venetians were very picky about where they formed colonies or conquered, they even rejected voluntary subjugation from states seeking protection from the Ottomans as they would simply drain resources.
The entire state of Venice was organised for profit from trade. It was highly centralised - everything was done for the betterment of the lagoon, the islands off the coast of Dalmatia and the likes of Crete, Modon-Coron and Negroponte were merely tools to be utilised. They had no interest in integrating native populations, converting them or granting them citizenship. Controlling Dalmatia and Modon-Coron allowed them to control the Adriatic, reducing piracy, Crete was a stop-off for merchants travelling from Constantinople or the Levant. It was all about controlling strategic points of trade. The fourth crusade ended up in Constantinople because of Venetian ambition, it didn't care about heretics, heathens or exporting Venetian ideals, it cared solely about how it could make more money.
No one but Genoa had the resources to compete with them on the seas, but many other nations could match them on land, why engage in expensive and potentially detrimental land battles to conquer land that would not aid in the improvement of their maritime empire? Manpower was always an issue for Venice - the city was small without much room to expand - they would regularly hire condottieri (mercenaries) to fight for them. With no interest in integrating local populations, hiring mercenaries to defend their territory would have proven too costly had they expanded inland.
When you put all that together you have:
With this in mind, there was no reason for them to expand inland, and Venice, at least, never really tried.
The vast majority of what I've written is covered in Roger Crowley's City of Fortune, which I would highly recommend.
There’s no “Golden Formula” for the establishment of a successful Thalassocracy, be it focused on a city-state or not. But on the specific topic of ability to project power in the mediterranean, I think it’s most useful to hone in on the characteristics of where and how that power was projected. I think you’ll find that power was imposed where local institutional characteristics made it possible, and not necessarily where the conquering power made a concentrated effort to do so.
As a starting point it’s important to point out that the urban-centric political organization was not only the basic institutional building block in Italy, but also in most of the mediterranean (with the added caveat that in the rest of the mediterranean, a stronger sort of feudo-monarchial organization typically existed besides of the city, while in Italy it was particularly weak if not absent). This means that the vast majority of mediterranean polities, inland or maritime, were not successful projectors of power. Or rather, not as successful as others were: a mercantile concession here, an outpost there, a well-fortified ring of surrounding boroughs could all feature in the political history of places like Ancona or Amalfi, without us considering them particularly successful. And if there were Italian polities which would become successful projectors of maritime power, they would necessarily be city-based (sure, we could point out that there was a Pope and a King in Italy, but the monarchy in the Southern Half of the peninsula was a particularly ineffective projector of power; while the Papacy’s mechanics of projecting coercive force and temporal power were surprisingly aligned with the mechanisms present in the rest of urban Italy).
And success could come in different forms at different moments in time: stretching our timeline back to the Athenians, over time they did emerge as the dominant power in Greece (sure, with the numerous caveats that come with that assertion); while focusing on our Italian examples, by the 15th century the Venetians had built a large and well-managed mainland state encompassing the whole of Northeastern Italy; while the Genoese, protected by high cliffs and steep ravines at their shoulders, came to dominate the whole of the coastline to the east and west of their center of power.
So here we are back to your question: Why were the Venetians and Genoese so much more successful as they turned “inland” compared to the Pisans, but also more successful than the Amalfitans, or who not even more successful than the Anconitans?
Tying into my lengthy introduction, part of the answer is that because these were already successful polities when compared to the whole roster of city-based institutions in their vicinity. The elaborate consensus-building government institutions in Venice, coupled with a rapidly specializing council-based system aiding executive decision-making, not only guaranteed the Venetians would avoid being reeled into the destructive conflicts which would scar the medieval Italian mainland, but also meant the Republic was poised to rapidly absorb a large swath of Northeastern Italy when the opportunity presented itself. The institutions in Venice would make the lagoon more resilient and prosperous than their rivals in Padua, Verona, and even Milan, where consensus-building institutions did appear, but did not become sufficiently developed to isolate destructive impulses imposed by influential decision-makers.
Genoa's story was slightly different, and while less successful than Venice, they nonetheless played an important role in the Western Mediterranean. So as we ask why they succeeded where their Tyrrhenian neighbors in Pisa did not, my actual answer focusing more on Genoa and Pisa can start, below: