One thing he wasn't doing, was playing around with the shards of Narsil.
Otherwise, well, "[Elrond's] house was perfect, whether you liked food, or sleep, or work, or story-telling, or singing, or just sitting and thinking, best, or a pleasant mixture of them all."
Remember, Boromir had some recuperating to do; his journey through Minhiriath and Eriador had been arduous, in fact remarkable, a real Bear Grylls feat.