Yes, travel insurance is worth carrying for a Montevideo city trip, even though this is one of the calmer destinations in this guide. Uruguay's capital has a well-regarded private healthcare sector by regional standards, so the honest case for coverage here leans toward cost and unfamiliar-system gaps rather than any dramatic danger along the Rambla or in the city center, and it is worth treating the trip with the same baseline preparation as any other international visit.
Private clinics in Montevideo handle most needs a visitor is likely to encounter, and public facilities exist as a backstop, but neither is free for a foreign visitor without the right cover. Check whether your existing health cover extends abroad and specifically to Uruguay before assuming it applies, since coverage rules differ by country of residence, and the page cannot know what your own plan or national scheme includes; many home plans quietly stop at the border regardless of how comprehensive they feel at home.
Most visitors spend their time along the Rambla, Montevideo's long waterfront promenade, and in the historic Ciudad Vieja district, and the city itself poses little unusual risk beyond ordinary urban travel such as pickpocketing in crowded tourist areas. The main weather event worth knowing about is a sudestada, a southeasterly storm surge off the Rio de la Plata that can flood low-lying coastal streets, including stretches of the Rambla, with limited warning at certain times of year, more a nuisance than a genuine danger for most visitors.
Keep any clinic invoice or treatment report and receipts for medication if you need care, since Uruguayan providers generally issue standard paperwork on request. Many policies also want notice before non-emergency treatment is booked, so check the claims process in your policy wording before you travel rather than assuming reimbursement is automatic once you are home, particularly for anything beyond a routine walk-in visit.