There are a number of walking trips to be done from St Ives, all depending on how far you want to go, and you can buy booklets in most bookshops as well as the tourist office and other places to guide you. The South West Coast Path which runs along the coast of England comes through St Ives so either side of town connects to it. One side (leading you along the northern coast of Cornwall if you would keep on walking) means that you set off from Porthminster Beach by the railway station and walk the 4 kilometres or so through Carbis Bay and perhaps onto Hayle in the inner part of the bay just before St Ives. You walk on the seaside of the railway which also runs on these leafy cliffs, and all the time you have a spectacular view of Hayle sands and of Godrevy Lighthouse.
On the other side of town, you start from the Tate Gallery/Porthmeor Beach area and walk past Clodgy Point up the hills where St Ives had its own mining once, and again with spectacular views of the Atlantic as you walk. Here you can go for a round trip of a few kilometres which takes you back into the town centre, or you can continue on the Coast Path to Zennor (see tip) and beyond if you have the energy. St Ives to Zennor is around 6 kilometres by road (but feels longer thanks to the serpentine style roads in the spectacular landscape) but with the ups and downs of hills and paths, the actual walk is more than 10 kilometres. Summertime, buses directly to and from St Ives stop in Zennor and other villages in this area if you want to walk one way and return by bus - just make sure you check timetables. Walking from Zennor to St Ives is the more downhill alternative...
Equipment: I already assume you wear sensible shoes if you intend to walk, but on the Porthmeor path it is perhaps particularly important due to holes and things left from the mining heydays so even if the paths are looked after it can be rough terrain since it is also a bit boggy, and especially if you walk in spring or after heavy rains. One of those booklets or even a proper Ordnance Survey map could also be useful for this one since you might want to know what you have in front of you from the mining days and why you have to make a detour in places. Even if the major path is signposted by the National Trust, it is easy to take the wrong turn and end up on other paths here and there on this one, and if the fog should strike, you will have other things than overgrown National Trust-signs to look out for.
Water is a must since there is no service for a good while on either walk (but a good pub in Zennor). Binoculars is something you might regret not bringing, since not only birds but also seals and dolphins can be spotted on either walk if you are lucky.
There are several surf schools with board and wetsuit rentals in the St Ives area. The one in the picture is the one at Porthmeor Beach, the surf friendly beach right in the town centre but that one does not seem to have a website, you just have to turn up and book. Here at Porthmeor, the real die hard surfers sometimes complain that they get too little space since the beach is very popular with families with body boarding kids, but if you are not too fussy about that, the waves themselves should be fine. Types of waves of course depend on the winds and on the tide but I have never seen Porthmeor without decent waves of some kind. The lifeguards summertime put up black and white surf flags where you can surf, whilst the red and yellow ones are for the swimmers and body boarders to stick to, so at least you have your own part of beach. The body board bit gets quite crowded on a good day just as described in the first link below but it is a fab beach. You can read more about it under my general St Ives tips where I describe the beach and its facilities.
In St Ives Bay also has what claims to be the oldest surfing school, the Gwithian Academy of Surfing, on the other side of the bay, past the little town of Hayle, so that could be another alternative if you have your own car and are not dependent on buses and trains to get around since that would take some time even if possible. Hayle has a longer stretch of beach so it is less crowded and also more directly westerly with reliable waves. As I said, there are loads more than these two but they get mentioned on central location and on merit. Below there is also a link giving you the surf weather for St Ives.
Equipment: You can rent wetsuits and big boards at the surf centres but wetsuits are also sold in a couple of places in Fore Street and the harbour area and children's body boards can be found in many more souvenir-, beach- and paper shops for just a few pounds.