Some “traditional” Freemasons claim that they are the originals with really the world-wide network that other (grand) lodges lack. This is a bit of a half argument.
On a small scale you see that many lodges rent the same building as other lodges. Often the building isn’t owned by one lodge, but by a foundation of sorts and they rent out the rooms to lodges. Costs can be spread, there is less time the building is empty. The lodges that work in the same building, usually have some form of contact, as agendas have to be harmonised for example. More and more frequently (at least in Europe) you see that different lodges have information evenings for prospective members together.
On a somewhat larger scale, within a country (or state), a grand lodge often has some sort of contact with other grand lodges. Some of them they may “recognise”, some they don’t. In the case that there is recognition, members can visit each others formal meetings.
Lastly, there are several large Masonic organisation in which grand lodges work together. Sometimes being member of such an organisation, requires “recognition”, meaning that when a grand lodge is member of an organisation such as Clipsas or AME/EMA there suddenly is an international network of lodges that you can visit.
Then of course there are many, many informal meeting places, on- and offline. There you will meet members, people who are interested, some will be interested in you and your (grand) lodge, others will not be. This isn’t really different within Freemasonry than within any community.
All in all it is fairly safe to say that in most cases you will have options to visit other lodges. This may be limited of a mixed gender lodge in the USA for example or quite the contrary. A Belgian member of Le Droit Humain can visit almost all Belgian lodges, while a member of a Regular Grand Lodge of Belgium can visit only 6% of Belgian lodges (only RGLB lodges, while LDH can visit lodges of most other grand lodges).
Something similar can be said worldwide. A European co-Mason won’t have many lodges to visit when (s)he travels to Scotland or the USA, but things are way different in France or South America. Indeed, also co-Masons do have a worldwide network. That network may be thinner in some countries as in others, but this also goes for “regular” Freemasons who will have a tiny network in Belgium or France and a large one in the USA or the UK.