The West Fjords is a great area of Iceland for general travel, spectacular scenery, feels remote, still relatively few tourists. Don't underestimate the distances, things are further than you think as the roads wind in and out of every fjord, but the scenery is great all the time so just enjoy. Yes, Látrabjarg is amazing, try to go there in the evening if you can as there is a good chance of seeing Arctic Fox. As for specific sites, just stop anywhere you think looks good really, there are birds pretty much everywhere in Iceland in May/June, although fewer breeding shorebirds than elsewhere due to the lack of lowlands there. There have been King Eiders in the Common Eider colony by the road in the village of Bíldudalur and there is often a King Eider at Hesteyri in Hestfjörður in summer https://ebird.org/hotspot/L1168114
. If you stay at Drangsnes, the road north of there up to Norðurfjörður, i.e. road 643, is absolutely fabulous, my favourite road in Iceland in many ways, no traffic and totally stunning, but it's a dead end and you have to return the same route (no bad thing). I've cycled the length of it twice in recent years and have had killer views of Gyr Falcon both times (Gyr can be seen elsewhere in the West Fjords too). You won't gain any birds you won't see elsewhere here but it's just so lovely (in good weather...). Should you skip it for more time in Borgarfjörður eystri, difficult as Borgarfjörður eystri is one of my favourite places in the east of Iceland and very much worth visiting. But it's a small area and you won't need much time there.