Montevideo is a city of distinct neighbourhoods, and where you lay your head decides a surprising amount about the trip you have. There's no single right answer — it depends whether you want the historic buzz of the old town, the beach-side ease of Pocitos, or somewhere quiet to sleep between days out — but a little thought here pays off across the whole stay.
Ciudad Vieja and Centro put you in the thick of it. Staying in or near the old town means the museums, the port market and the grand streets are on your doorstep, along with a good chunk of the nightlife; it's atmospheric and central, if a little quiet in patches after dark. This is the choice for first-timers who want to be able to walk to the sights.
Pocitos and Punta Carretas are the easy-living option. These leafy beach-side neighbourhoods east of the centre swap history for a relaxed, residential feel — the Rambla and the sand at the end of the street, good cafés and restaurants, and a safe, pleasant sense of everyday Montevideo. Many travellers who intend a short stay end up extending it from a base here.
Match the type of place to your budget and mood. Montevideo does the full range: sociable hostels with the traveller crowd and a kitchen to share, mid-range apartment rentals that suit couples and longer stays, and a growing handful of boutique hotels in restored old-town buildings. Out of peak summer, prices are gentle by South American capital standards, and you get a lot for your money.
Whatever you choose, book the beach-season weeks ahead. Montevideo itself never quite sells out the way the coast does, but the best-value places in Pocitos and the characterful old-town boutiques do fill for the summer and the odd festival, so plan ahead if you're coming December to February. Off-season, you can be far more spontaneous — and the city is arguably at its most charming then anyway.