Although I normally carry a tent, given the choice, I will usually opt for a real bed if it is reasonably priced. This page contains information on some of places I have stayed that I feel obliged to mention because of the combination of service, price, location or bike friendliness.
I only list places that really make an effort and most of the places recommended are unaware I have even listed them. Hopefully you will receive the same service I did, but please let me know if you have any feedback to add.

Copenhagen Amager Hostel - Vejlandsallé 200, 2300 København S, Denmark
Whilst hostels make the ideal low cost, not-tent based, accommodation when touring, I wouldn't normally feel compelled to recommend many of them, but this one is worth it!
Very friendly staff, excellent bike security, good quality beer served until late and none of the austere attitude of some hostels.
Very glad I changed my mind about using the city hostel (which has no facilities for cyclists.)

Lomamaja Pekonen - Lahenrannatie 10, 99300 Muonio, Finland
For £10 (less than the cost of a tent pitch in some places) I got a cabin with bed, electricity, showers and a sauna (had I wanted it) as well as a friendly service.
The lakeside location affords a lovely vista, but beware the mosquitoes!

FJT - 'Le Vénasque' - 3 Rue de la Résidence, BP 158, 31804 Saint-Gaudens, France
Yes its a hostel and yes its basic, but all the rooms seem to be singles with en suite facilities and plenty of power sockets, so it feels more like a hotel (apart from providing/hiring your own sheets).
Also has restaurant facilities, so you can get a nights sleep, dinner and breakfast for under 20 euros!

Hôtel du Château - 7 av Mondenard, 47600 Nerac, Fance
Contact: Hôtel du Château
Phone: +33 5 53 65 09 05
Email: N/A
Web Site: N/A
Very friendly hotel and reasonably priced (£20) for a double room with a balcony.
The bike was securely stowed indoors in the reception area and the set menu was plentiful, inexpensive and delicious!
Just a shame I couldn't find better contact information.

Gistiheimilid Geysir - Haukadalur 3, IS-80, Selfoss, Iceland
Contact: Águsta Thorisdottir
Phone: +354 486 8733
Email: agustath@visir.is
Web Site: N/A
A great place to stay in a fantastic location and, by Icelandic standards, very reasonably priced. Agusta is friendly and (of course) fluent in English.
Bikes can be left round the side of the building, they wont be covered but will be safe (no-one ever steals a bike in Iceland anyway.)

Nordkapp Camping - Skipsfjorden, N-9751 Honningsvåg, Norway
Friendly, family run site, with a choice of, very reasonably priced, camping, hostel or log cabin accommodation.
Skipsfjorden is a little north of Honningsvåg and (tacky tourist centre aside) about as close to Nordkapp as civilisation gets; making it a good base to start or end from.

Low Kirkbride Farm - Auldgirth, Dumfries & Galloway, Scotland. DG2 0SP
A little remote but worth it! The only place to greet us with pots of tea and homemade cakes. Evening meal available by prior arrangement as well as a hearty breakfast and packed lunch.
Bikes can be left in a cattle shed and will be safe because you are miles from anywhere!

Tordarroch - Castle Street, Dornoch, Scotland. IV25 3SN
Tordarroch is a nice place and Rose is very helpful (even offering to dry our laundry for us.) The packed lunch we had prearranged and breakfast were both of a good quality.
Our bikes were safely stored in the back garden, the tarpaulin offered to cover them was not required.

Hotel Robert - Av. de Catalunya, 1 - 08787, La Pobla de Claramunt, Spain
Probably just about the plushest hotel I have stayed in while touring (monogrammed towels and bath-robes), but without a matching price tag! (About £20 for a single room)
The staff were all very friendly, bike storage was covered and secure and the breakfast was all you can eat to boot!

Hotel Gillet - Tingshusgaten 10, 641 45, Katrineholm, Sweden
Okay expensive compared to camping, but reasonable by Swedish hotel standards and sometimes you need a little luxury!
Friendly, comfortable, bike safely stowed in garage, good breakfast and an interesting art collection.

Swiss Hostel Daschen - Schloss Laufen am Rheinfall, 8447, Dachsen, Switzerland
Again youth hostels whilst functional are not normally noted for excellence, but this one deserves a mention. It is actually situated in the Schloss overlooking Rheinfall.
It has good facilities for cyclists and is run by a host who clearly loves his work! The three abreast dormitory bunk beds were a new one on me and might be a little too close for comfort in the busy season!