Someone ring for me?

There are many of these types of services:
1. Some are actual buildings that have larger rooms and cater to people wanting to spread out. These are actually chains, and I'd say designed for a week. Examples are Extended Stay America.

2. There are some services that will search for an open apartment for a traveler that will be away for a month or more. Examples include a program by Marriott which I forget the name of. There are many by region, so I recommend a search engine to find one of these.

3. Some buildings will lease space for a short period of time (relatively short...). I'm currently in a building in HKG on a soon to expire 6 month contract. I found this place through a Marriott program actually (not the one listed above, though).

4. Some hotels rent out apartments for guests. For example, the Grosvernor House in London has several multi-bedroom apartments that it leases/rents. I'm currently looking into the I-C Sydney, which has a single 2-bdrm apartment they lease out.

Here's what I do:
1. Short Visit (less than 2 weeks): Live out of hotel, possibly suite-type hotel.

2. Month-long: Consider a short-term lease, like the I-C Sydney apartment.

3. Half-a-year: Consider a program that finds you a real apartment.

4. Multi-year: Rent an apartment on a long time lease.

5. Buy a property (I only own one property....)

Oxford