Leuven is an easy Belgian city to do with a dog: a compact walkable historic centre, the dense Flemish brown-café culture of the Oude Markt, Brussels Airport BRU 18 minutes away by direct dog-free NMBS train, the Heverleebos and Meerdaalwoud forests on the doorstep, and a strategic position as the closest sizeable Belgian city to the Trappist beer tour route.
April-June and September-October are ideal, average highs 14-22 °C, the Heverleebos forest in full leafy bloom and the Oude Markt terraces lively without midsummer student-festival saturation. Avoid the KU Leuven 'Beiaardcantus' end-of-academic-year nights in May and the first weekends of September (massive student influx); winter is quiet, wet but magical with the Winter in Leuven Christmas market that admits leashed dogs.
Leuven is the closest sizeable Belgian city to the Trappist Beer Tour route: Westvleteren, Westmalle, Achel, Rochefort, Chimay and Orval are all reachable in a day by free-dog NMBS train and a short taxi. Hoegaarden white-beer brewery is 7 km west by bus 358. Day trips: Brussels in 25 min, Antwerp in 50 min, Ghent in 1h05, Liège in 50 min, Bruges in 1h15 via Brussels. Brussels Airport BRU in 18 min for arrivals and departures.
Belgium uses the euro. Most hotels and restaurants accept Visa/Mastercard, contactless is universal. Pet supplements at Leuven hotels average 10-20 EUR per night, in line with the EU median and slightly below Brussels; tipping is not obligatory but rounding up 5-10% in cash is standard for good service.