Resources: http://www.japan-guide.com/e/e2164.html http://www.tourism.metro.tokyo.jp/english/

Where should I stay?
I always recommend a hotel which is a short walking distance from any station on the JR Yamanote Line. This includes Shinjuku, Shibuya, Ikebukuro, Ueno, Akihabara, etc
Why?
Shinjuku, Shibuya and Harajuku, which are the most popular shopping destinations in Tokyo, are conveniently located on the JR Yamanote line.Plus it's easy access to Odaiba bay and Ueno Park.
It's a little tricky to get to Asakusa and Tsukiji area, but it's still very do-able.

Budget accomodations can be found in Asakusa area, Ueno, Ikebukuro and areas slightly off from JR Tokyo station.Shinjuku and Shibuya areas though popular, are relatively more expensive on normal basis.

My personal favourite is Ikebukuro, I'm in love with that place :)

What are my lodging options?
*note that my examples are not recommendations, and are not the full listings.

Business Hotel
The most popular and the most common type.
You can say it's a low-end hotel, but it's still clean and pleasant to stay in.
They do offer breakfast options as well.
A small number of business hotels do not offer private toilet and bath facilities, instead there is a common toilet and bath which all the guests share.
As they actually cater for Japanese Businessmen, they tend to be very close to a train station.

Prices range from 5000 - 18000yen

Examples:

1. Renaissance Hotel Chain
2. Hotel Strix　(my personal Tokyo favourite)
3. Shibuya City
4. Sunroute Hotel Chain

Hotel
These tend to be on the high end in price.
The rooms are definately bigger than the Business Hotels.

Prices range from 15000yen - 50000yen

Examples

1. Prince Hotel Chain
2. Ritz Carlton

Minshuku
These are family-run establishments. Something like the bed and breakfast concept in the west.
They are cheap and good, but most of them do not have private toilet and bath facilities, instead there is a common toilet and bath which all the guests share.
Prices for rooms are usually charged per person per night, which is also why most places do not offer rooms for just 1 person.
But it's a good option for large groups who want to save money and share a single room.
Rooms are usually done up japanese style.
As the prices get cheaper, they tend to be a little out of the way.

Prices range from 2500yen - 15000yen

Example

1. House Ikebukuro
2. New Izu Hotel
3. Aizuya Inn
4. Homeikan

Guest Houses and Hostels
These came up as part of the Minshuku concept, but are managed like a Hotel.
As with the Minshukus, they are cheap and good, but most of them do not have private toilet and bath facilities, instead there is a common toilet and bath which all the guests share.
For Hostels, you may not get a private room facility, instead it's a common room with common facilities.
As the prices get cheaper, they tend to be a little out of the way.

Prices range from 1000 - 15000yen

Example

1. Oakhouse
2. Khaosan
3. Sakura Hostel

Ryokans
To be honest, Ryokans in Tokyo are few and far between. And are very unlike the ones you watch on Japan Hour.
These are the high end versions of the Minshuku. The rooms are ALWAYS in japanese style and usually offer breakfast as part of the room stay, and sometimes offer dinner (which is different from the usual Ryokans that offer dinner on a usual basis).
Ryokans that offer western rooms or mixed style rooms are usually called Ryokan Hotels.
They are cheaper than the Ryokans you would find in onsen towns and they also would most probably not provide onsens. At the most you'll get a sento.

Price range from 12000 - 40000yen

Examples

1. Ryumeikan chain
2. Sumisho (has sento)
3. Asakusa Shigetsu (has sento)
4. Sadachiyo SukerokunoYado

Weekly Mansions
These are apartments where you can rent for at least 7days.
The lodgings have a kitchen and living area provided. Housekeeping services are also included, and you will have to pay for electric and heating.
But you won't have any meals, and most of the sites to book from are in Japanese.

Price range is about 3000-12000yen per night for a 7 day stay

Examples

1. Weekly Center
2. Weekly Monthly

Please check out my post on Accomodation Booking