The Cincinnati Reds made their first ever trip to Safeco Field (or Seattle at all) and routed the Mariners 16-1. That surpassed, as far as I can tell now, the record for the most runs scored by a team in its first visit to any stadium.
Back on May 28, 1993, the Philadelphia Phillies visited Mile High Stadium for the first time and hung up a 15 on the Colorado Rockies, winning 15-9. The Phillies won the next day 6-0 and then swept the series with an 18-1 win.
When the Phillies visited Coors Field for the first time in 1995, they scored just five runs and lost 8-5.