Personally, I'd head straight to the Moda center, formerly known as the Rose Garden, and watch some NBA basketball. I cherish any chance to boo Gerald Henderson, who I was very happy to see traded away. Also, watching Damien Lillard is always a good time for a fan of the sport.
But that's just me. You did also say you wanted to know the most beautiful place to visit. That's a little subjective, but if you're willing to venture just a little outside the city, there's a great spot you shouldn't miss: Multnomah Falls.
These falls are are a two-tier waterfall with a bridge crossing the river. The upper falls are 542 feet, and the lower ones are 69 feet. Multnomah Falls is the largest waterfall in Oregon, and possibly the second tallest year-round waterfall in the United States.
The site is popular with photographers and a common site of weddings. It's in the Columbia River Gorge, east of Portland.
"Multfalls" by Kelvin Kay w:User:Kkmd - w:File:Multfalls.jpg. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Multfalls.jpg#/media/File:Multfalls.jpg