Ive been to both Alcudia & turkey a couple of times. Theres some decent trips but theyre a lot more expensive than Turkey. Cheapest way to do it is if you're prepared to sit through one of the blanket trips for an hour at start. I went the big Majorca trip orange express (train), boat & bus all day for about £20 each

From Puerto Pollensa (and maybe also Alcudia, I'm not certain, BUT SEE NOTE BELOW) you can get a boat out to either of Playa Formentor or Cap Formentor. The former allows you to get off and spend some hours at the beach before returning either by bus or boat. The boat/bus trip gives you spectacular views of the north western cape of the island. These are public services so you can do it completely independently and very cheaply. There is a regular, every 15 mins, bus service Alcudia to Puerto Pollensa.
Personally, having spent several holidays in Turkey and many in Mallorca, I think you will not be disappointed.
Costs from Alcudia via Puerto Pollensa to Playa Formentor (per person one-way)...
Bus Alcudia to PP 1.20 Euros.
Boat PP to Playa Formentor 5 Euros.
Bus Playa Formentor to PP 1.10 Euros (limited service, 2 buses in the afternoon, none on a Sunday).
Bus PP to Alcudia 1.20 Euros.

Another option (as posted above) is the "Orange Train" from Soller down to Palma. Again you can do this independently. Bus to Puerto Soller, tram up to Soller, train to Palma, bus to Alcudia.

Of course all these trips can be done through an agent.

This an extract from the website...
http://www.majorca-mallorca.co.uk/alcudia_attractions.htm
...In addition to the standard "see Majorca in a day" type trips run by most of the major tour operators, a good selection of 1/2 day boat trips runs most days from the main port area. The cost is around £12 for adults and £6 for children, including lunch, and takes you up the coast to a secluded beach at the tip of Formentor. The boats are quite modern, with both a small bar and toilet facilities onboard. On most trips the captain will usually stop for about 30 minutes giving you the chance to dive or jump off the back of the boat and cool off in the sea.

Blanket Tour....YUK!

Mallorca... Disfruta! (Spanish for Enjoy!)

Hi.
Yes there are boat trips from Alcudia which go to Playa Formentor, Cap de Formentor and Cala San Vicente here is their website, The trip to Playa Formentor stops in a small bay for passengers to have a swim, then stays at Playa Formentor for about 90 minutes before returning: http://www.tmbrisa.com/engl/indexcast.html.
Also there are boat trips from Cala Bona to Cala Rajada, Cala Millor, Sa Coma / S'Illot, Porto Cristo, Calas de Mallorca and Cala Romantica. here are two websites for the companies operating in this area:
http://www.crucerosbarcelo.com/indexi.html
http://www.illabalear.com/INGLES/Iindex.html
There are also boat trips from Palma to various resorts:
http://www.cruceroscostadecalvia.com/nueva/index.php
We can highly recommend the boat trips from Alcudia and Cala Bona, but in October when there is a bit more wind you might find a fair few cancellations.
As for Horse riding there are plenty stables to choose from, but I think the biggest in the Alcudia area is Rancho Grande on the main Arta - Alcudia road (MA12), here is their website: http://www.ranchograndemallorca.com/english/index.php
I know there are stables in Sa Coma but cannot remember the name.
Hope this helps.
BigAL