Getting to Tilos
Regularly updated ferry schedule: http://tilos-travel.com/tilos_ferry_schedules.php
The Dodecanese Express and Blue Star link Tilos with airports at Rhodes and Kos.
Summer-only link to Kamiros Skala in Rhodes: http://gonisyros.gr/en/passengers-en/ship-itineraries-en.html
Places to stay in Tilos
Renting a house or apartment on Tilos is quite easy, whether you want to stay for a few days or a few months. I can often make recommendations, depending on your needs.
Megalo Horio has three places to eat and drink, open year-round - the Kafeneion, To Kastro and Kali Kardia - as well as a couple of shops. Beaches within walking distance are Eristos and Ayios Antonis (half an hour), Skafi (45 minutes) and Plaka (easier by scooter).
Milios studios: http://milios-studios.gr/
There are two artists whose work you can view and buy. Angeliki Stringou is right at the top of the village by the higher of the two churches, and her studio is open from 11am to 7.30pm. - she paints local wildlife and people:
... while Pierre's studio is at the bottom of the village on the way to Eristos.
Eristos Beach Hotel: http://www.eristosbeachhotel.gr/pageseng/default.aspx
Nitsa Apartments: http://nitsa-tilosapartments.com/
Filoxenia on the road to Eristos: https://www.facebook.com/filoxenia.tilos
This tiny harbour has two tavernas, Elpida and Delfini, open in the summer only, and two places to stay, a house on the waterfront and Antonis Apartments - I'm happy to pass along enquiries for either.
Livadia is the port and biggest village, with numerous places to eat and stay.
Stefanakis Villas: Stelios Stefanakis can also rent you a car or sell you a ferry ticket!
Michalis Studios: http://www.michalis-studios.gr/
Going via Rhodes/Kos?
Search this blog for things I like in Rhodes. The Old Town has a fantastic Archaeological Museum. If you have time to spare, visit this cafe in a restored traditional house, next to the church of St Fanourios: www.angelacastle.gr
If you're looking for a lovely place to stay in Rhodes, try:
Nikos Takis Hotel http://www.nikostakishotel.com/
Spirit of the Knights Hotel http://www.rhodesluxuryhotel.com/
For something simpler and easier on the budget, try the Savoy Hotel in Mandraki - the airport bus leaves from just nearby - or Knights of the Old Town.
A lovely, great-value place to stay in Kos is the Kosta Palace on the harbour. There are fish tavernas around the corner, e.g. Sardelles.