We've had 2 people stay somewhat regularly, 3 in a few occasions, and we've anticipated up to 4. We're in a 1BR, though nominally somewhat larger than yours. We are also close to your niece's age, and like being able to have people stay, so our LR couch is a futon. Third person (or if 2 don't want to share) has generally been offered camping gear and floor space. We recently got a free airbed from a friend but haven't used it at home.
The key, though, is that we generally like having people stay. It tires me (introvert) out eventually, so we can't/wouldn't do it all the time, but it's something we're happy to do for family and friends who make the effort to visit, if they are satisfied with the level of accommodations. Bf's parents &sis didn't take us up on it and stayed down the street...We aren't certain if religious beliefs (re: cohabitation), desire for comfort, or not wanting to impose was the dominant reason.
I think any of the options you listed sound fine, but asking a relative to pay their own accommodation while visiting you might elicit negative feelings, esp if they are harder pressed to afford it and/or might be interested in saving money at the expense of comfort (which should be something we support here, hmm?) Something to consider in context of whether you might like to be closer to your niece, how much of their visit is about you vs local attractions, their personality/attitude, and what you know about their financial situation.
My 2 cents...
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