Well, then, have you considering paying for an affordable indie hotel for some nights?

I find that more practical than Priceline if that's all I'm looking for. Priceline tends to lower luxury hotels to affordable prices, but luxury hotels tend to nickel & dime you. For the same price booked without any tricks you can often find an indie hotel which will provide lots of stuff for free that a luxury hotel will nichel & dime you on.

There are affordable indie hotels in many cities.

The thing I do, when I don't find a hotel in a European city that I can get on points that I want to get (ie, sometimes I have the points but the hotels on points are just too poor a value), I'll go to www.tripadvisor.com, look at the hotels in the order they give (by order of recommendations), but visually scan the "typical price" they show for most hotels and look for the ones with reasonable prices. Then I look at the reviews and see it the hotel itself seems reasonable. Then I click on show prices (I personally tend to use only booking.com because it doesn't tend to charge me upfront and usually has very reasonable cancellation policies) and see what actual prices are available for the dates you need.

On a trip I'm planning to eastern Switzerland and western Austria, I just used this technique to find very affordable (in most cases much less than $100 a night for a single, though a double might have been a bit more in some cases) hotels with free breakfast and free internet in Appenzell, Switzerland (where there are no hotels on points at all) and in Zell am See, Austria (where again there are no hotels on points at all).

But you could use this same technique in bigger cities, too. (There's just a whole lot more hotels to sort through in a huge city like London than in a small town! )

Alternately, you could use guidebooks such as Rick Steves or Lonely Planet for indie affordable indie hotel recommandations.