Internet access is widely available in all towns and cities. All midrange and top-end hotels, bar a few remote ecolodges, have wi-fi available (often in room but sometimes just around the reception area) and an increasing number of budget hotels, restaurants and cafes offer wi-fi. However, speeds are slow and service is often cut off for no reason.
A good alternative (or supplement) to hotel-provided wi-fi is to buy a local SIM card with data or an internet dongle from any of the main mobile-phone providers (MTN offers the best network coverage). This means you'll be able to get online in all but the most remote corners of Rwanda.