Neum is Bosnia's only coastal town and - to be completely transparent - it is not the most beautiful of seaside resort. It's still a good base though if you want to explore the Croatian coast and have a more affordable accommodation or if you are generally looking for a cheaper beach holidays on the Adriatic.
Be aware that the beaches in Neum, like in Croatia, are pebbles so bring flip flops.
When in Neum, we always stay in a different apartment and I cannot really recommend any of them – just book your own accommodation, you will not spend a lot of time indoors anyway. Since Neum is very hilly, be careful when booking, otherwise you might be climbing hundreds of stairs in the midday heat!