Can anybody tell me if taxis are plentiful at Monaco train station & I f so, how far is Le Meridien hotel?
The taxi service in Monaco is a national embarrassment. You would be most unlikely to find one for a journey within Monaco, the wait is generally ridiculously long. The reason for this is licensing: there are only 82 taxi licences in the whole Principality, for a population of over 36,000, not to mention the tourist and business trade. In such short supply, small wonder taxi drivers don’t bother to get out of bed for less than an airport run.
Instead, exit the station at Pont Ste Devote (the highest exit), cross the road and pick up bus number 5 heading to Larvotto. The stop you need is Sea Club, right after Plages. And to answer your specific question, not very far; the whole Principality is only two square kilometres in size.